| 1. |
- Agirre, Jon, et al.
(author)
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The CCP4 suite: integrative software for macromolecular crystallography
- 2023
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In: Acta Crystallographica Section D. - : INT UNION CRYSTALLOGRAPHY. - 2059-7983. ; 79, s. 449-461
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Journal article (peer-reviewed)abstract
- The Collaborative Computational Project No. 4 (CCP4) is a UK-led international collective with a mission to develop, test, distribute and promote software for macromolecular crystallography. The CCP4 suite is a multiplatform collection of programs brought together by familiar execution routines, a set of common libraries and graphical interfaces. The CCP4 suite has experienced several considerable changes since its last reference article, involving new infrastructure, original programs and graphical interfaces. This article, which is intended as a general literature citation for the use of the CCP4 software suite in structure determination, will guide the reader through such transformations, offering a general overview of the new features and outlining future developments. As such, it aims to highlight the individual programs that comprise the suite and to provide the latest references to them for perusal by crystallographers around the world.
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| 2. |
- Bannikova, Anna A., et al.
(author)
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Who are you, Griselda? A replacement name for a new genus of the Asiatic short-tailed shrews (Mammalia, Eulipotyphla, Soricidae) : molecular and morphological analyses with the discussion of tribal affinities
- 2019
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In: ZooKeys. - : Pensoft Publishers. - 1313-2989 .- 1313-2970. ; :888, s. 133-158
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Journal article (peer-reviewed)abstract
- The first genetic study of the holotype of the Gansu short-tailed shrew, Blarinella griselda Thomas, 1912, is presented. The mitochondrial analysis demonstrated that the type specimen of B. griselda is close to several recently collected specimens from southern Gansu, northern Sichuan and Shaanxi, which are highly distinct from the two species of Asiatic short-tailed shrews of southern Sichuan, Yunnan, and Vietnam, B. quadraticauda and B. wardi. Our analysis of four nuclear genes supported the placement of B. griselda as sister to B. quadraticauda / B. wardi, with the level of divergence between these two clades corresponding to that among genera of Soricinae. A new generic name, Parablarinella, is proposed for the Gansu short-tailed shrew. Karyotypes of Parablarinella griselda (2n = 49, NFa = 50) and B. quadraticauda (2n = 49, NFa = 62) from southern Gansu are described. The tribal affinities of Blarinellini and Blarinini are discussed.
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| 3. |
- Bouarroudj, Sofiane, et al.
(author)
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Classification of Simple Lie Superalgebras in Characteristic 2
- 2021
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In: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 2023:1, s. 54-94
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Journal article (peer-reviewed)abstract
- All results concern characteristic 2. We describe two procedures; each of which to every simple Lie algebra assigns a simple Lie superalgebra. We prove that every simple finite-dimensional Lie superalgebra is obtained as the result of one of these procedures. For Lie algebras, in addition to the known “classical” restrictedness, we introduce a (2,4)-structure on the two non-alternating series: orthogonal and Hamiltonian vector fields. For Lie superalgebras, the classical restrictedness of Lie algebras has two analogs: a 2|4-structure, which is a direct analog of the classical restrictedness, and a novel 2|2-structure—one more analog, a (2,4)|4-structure on Lie superalgebras is the analog of (2,4)-structure on Lie algebras known only for non-alternating orthogonal and Hamiltonian series.
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| 4. |
- Bouarroudj, Sofiane, et al.
(author)
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Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov)
- 2023
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In: Symmetry, Integrability and Geometry. - 1815-0659. ; 19
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Journal article (peer-reviewed)abstract
- Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such that for each root, there is minus it of the same multiplicity) and of ranks less than or equal to 8—most needed in an approach to the classification of simple vectorial Lie superalgebras (i.e., Lie superalgebras realized by means of vector fields on a supermanifold),—we list the outer derivations and nontrivial central extensions. When the conjectural answer is clear for the infinite series, it is given for any rank. We also list the outer derivations and nontrivial central extensions of one series of non-symmetric (except when considered in characteristic 2), namely periplectic, Lie superalgebras—the one that preserves the nondegenerate symmetric odd bilinear form, and of the Lie algebras obtained from them by desuperization. We also list the outer derivations and nontrivial central extensions of an analog of the rank 2 exceptional Lie algebra discovered by Shen Guangyu. Several results indigenous to positive characteristic are of particular interest being unlike known theorems for characteristic 0, some results are, moreover, counterintuitive.
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| 5. |
- Bouarroudj, Sofiane, et al.
(author)
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DIVIDED POWER (CO)HOMOLOGY. PRESENTATIONS OF SIMPLE FINITE DIMENSIONAL MODULAR LIE SUPERALGEBRAS WITH CARTAN MATRIX
- 2010
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In: Homology, Homotopy and Applications. - 1532-0073 .- 1532-0081. ; 12:1, s. 237-278
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Journal article (peer-reviewed)abstract
- For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we explicitly give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super) algebras with indecomposable Cartan matrix in characteristic 2 (and - in the arXiv version of the paper - in other characteristics for completeness of the picture). In the modular and super cases, we define notions of Chevalley generators and Cartan matrix, and an auxiliary notion of the Dynkin diagram. The relations of simple Lie algebras of the A, D, E types are not only Serre ones. These non-Serre relations are same for Lie superalgebras with the same Cartan matrix and any distribution of parities of the generators. Presentations of simple orthogonal Lie algebras having no Cartan matrix (indigenous for characteristic 2) are also given.
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| 6. |
- Bouarroudj, Sofiane, et al.
(author)
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Lie algebra deformations in characteristic 2
- 2015
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In: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 22:2, s. 353-402
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Journal article (peer-reviewed)abstract
- Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved Z/2-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every Z/2-graded simple Lie algebra in characteristic 2 is illustrated by seven new series. Type-2 algebras and one of the two type-4 algebras are demystified as nontrivial deforms (the results of deformations) of the alternate Hamiltonian algebras. The type-1 Kaplansky algebra is recognized as the derived of the nonalternate version of the Hamiltonian Lie algebra, the one that preserves a tensorial 2-form. Deforms corresponding to nontrivial cohomology classes can be isomorphic to the initial algebra, e.g., we confirm Grishkov's implicit claim and explicitly describe the Jurman algebra as such a semitrivial deform of the derived of the alternate Hamiltonian Lie algebra. This paper helps to sharpen the formulation of a conjecture describing all simple finite-dimensional Lie algebras over any algebraically closed field of nonzero characteristic and supports a conjecture of Dzhumadildaev and Kostrikin stating that all simple finite-dimensional modular Lie algebras are either of standard type or deforms thereof. In characteristic 2, we give sufficient conditions for the known deformations to be semitrivial.
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| 7. |
- Bouarroudj, Sofiane, et al.
(author)
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New Simple Lie Algebras in Characteristic 2
- 2016
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In: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; :18, s. 5695-5726
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Journal article (peer-reviewed)abstract
- Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].
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| 8. |
- Bouarroudj, Sofiane, et al.
(author)
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Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
- 2020
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In: Symmetry, Integrability and Geometry. - 1815-0659. ; 16
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Journal article (peer-reviewed)abstract
- We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformations. For all 15 Weisfeiler gradings of the 5 exceptional families, and one Weisfeiler grading for each of 2 serial simple complex Lie superalgebras (with 2 exceptional subseries), we describe their characteristic-2 analogs - new simple Lie algebras. Descriptions of several of these analogs, and of their desuperizations, are far from obvious. One of the exceptional simple vectorial Lie algebras is a previously unknown deform (the result of a deformation) of the characteristic-2 version of the Lie algebra of divergence-free vector fields; this is a new simple Lie algebra with no analogs in characteristics distinct from 2. In characteristic 2, every simple Lie superalgebra can be obtained from a simple Lie algebra by one of the two methods described in arXiv:1407.1695. Most of the simple Lie superalgebras thus obtained from simple Lie algebras we describe here are new.
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| 9. |
- Chapovalov, Danil, et al.
(author)
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THE CLASSIFICATION OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS
- 2010
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In: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 103-161
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Journal article (peer-reviewed)abstract
- We say that an indecomposable Cartan matrix A with entries in the ground field is almost affine if the Lie (super) algebra determined by it is not finite dimensional or affine (Kac-Moody) but the Lie sub(super) algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting on the main diagonal, is the sum of finite dimensional or affine Lie (super) algebras. A Lie (super) algebra with Cartan matrix is said to be almost affine if it is not finite dimensional or affine (Kac-Moody), and all of its Cartan matrices are almost affine. We list all almost affine Lie superalgebras over complex numbers with indecomposable Cartan matrix correcting two earlier claims of classification.
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| 10. |
- Iyer, Uma N., et al.
(author)
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PROLONGS OF (ORTHO-)ORTHOGONAL LIE (SUPER)ALGEBRAS IN CHARACTERISTIC 2
- 2010
-
In: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 253-309
-
Journal article (peer-reviewed)abstract
- Cartan described some of the finite dimensional simple Lie algebras and three of the four series of simple infinite dimensional vectorial Lie algebras with polynomial coefficients as prolongs, which now bear his name. The rest of the simple Lie algebras of these two types (finite dimensional and vectorial) are, if the depth of their grading is greater than 1, results of generalized Cartan-Tanaka-Shchepochkina (CTS) prolongs. Here we are looking for new examples of simple finite dimensional modular Lie (super) algebras in characteristic 2 obtained as Cartan prolongs. We consider pairs (an (ortho-)orthogonal Lie (super) algebra or its derived algebra, its irreducible module) and compute the Cartan prolongs of such pairs. The derived algebras of these prolongs are simple Lie (super) algebras. We point out several amazing phenomena in characteristic 2: a supersymmetry of representations of certain Lie algebras, latent or hidden over complex numbers, becomes manifest; the adjoint representation of some simple Lie superalgebras is not irreducible.
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