| 1. |
- Abdallah, Nancy, et al.
(author)
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Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four
- 2024
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In: Journal of symbolic computation. - 0747-7171 .- 1095-855X. ; 121, s. 102257-102257
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Journal article (peer-reviewed)abstract
- In (Stanley, 1978), Stanley constructs an example of an Artinian Gorenstein (AG) ring A with non-unimodal H-vector (1,13,12,13,1). Migliore-Zanello show in (Migliore and Zanello, 2017) that for regularity r=4, Stanley's example has the smallest possible codimension c for an AG ring with non-unimodal H-vector.The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal H-vector fails to have WLP. In codimension c=3 it is conjectured that all AG rings have WLP. For c=4, Gondim shows in (Gondim, 2017) that WLP always holds for r≤4 and gives a family where WLP fails for any r≥7, building on Ikeda's example (Ikeda, 1996) of failure for r=5. In this note we study the minimal free resolution of A and relation to Lefschetz properties (both weak and strong) and Jordan type for c=4 and r≤6.
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| 2. |
- Abdallah, Nancy, et al.
(author)
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Limits of graded Gorenstein algebras of Hilbert function $$(1,3^k,1)$$
- 2024
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In: European Journal of Mathematics. - 2199-675X .- 2199-6768. ; 10:1
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Journal article (peer-reviewed)abstract
- Let R= k [x, y, z], the polynomial ring over a field k. Several of the authors previously classified nets of ternary conics and their specializations over an algebraically closed field, Abdallah et al. (Eur J Math 9(2), Art. No. 22, 2023). We here show that when k is algebraically closed, and considering the Hilbert function sequence T =(1,3(k),1), k >= 2 (i.e. T = (1, 3, 3, ... , 3, 1) where k is the multiplicity of 3), then the family GT parametrizing graded Artinian algebra quotients A = R/I of R having Hilbert function T is irreducible, and G(T) is the closure of the family Gor(T) of Artinian Gorenstein algebras of Hilbert function T. We then classify up to isomorphism the elements of these families Gor(T) and of G(T). Finally, we give examples of codimension 3 Gorenstein sequences, such as (1, 3, 5, 3, 1), for which G(T) has several irreducible components, one being the Zariski closure of Gor(T).
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| 3. |
- Abedin, Raschid, et al.
(author)
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Topological Lie Bialgebras, Manin Triples and Their Classification Over g[[x]]
- 2024
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In: Communications in Mathematical Physics. - 1432-0916 .- 0010-3616. ; 405:1
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Journal article (peer-reviewed)abstract
- The main result of the paper is classification of topological Lie bialgebra structures on the Lie algebra g[[x]] , where g is a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0. We introduce the notion of a topological Manin pair (L,g[[x]]) and present their classification by relating them to trace extensions of F[[x]] . Then we recall the classification of topological doubles of Lie bialgebra structures on g[[x]] and view it as a special case of the classification of Manin pairs. The classification of topological doubles states that up to an appropriate equivalence there are only three non-trivial doubles. It is proven that topological Lie bialgebra structures on g[[x]] are in bijection with certain Lagrangian Lie subalgebras of the corresponding doubles. We then attach algebro-geometric data to such Lagrangian subalgebras and, in this way, obtain a classification of all topological Lie bialgebra structures with non-trivial doubles. For F= C the classification becomes explicit. Furthermore, this result enables us to classify formal solutions of the classical Yang–Baxter equation.
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| 4. |
- Afshari, Bahareh, 1981, et al.
(author)
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Abstract Cyclic Proofs
- 2024
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In: Mathematical Structures in Computer Science. - 0960-1295 .- 1469-8072.
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Journal article (peer-reviewed)
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| 5. |
- Afshari, Bahareh, 1981, et al.
(author)
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Cyclic proofs for the first-order mu-calculus
- 2024
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In: Logic Journal of the IGPL. - : Oxford University Press (OUP). - 1367-0751 .- 1368-9894. ; 32:1, s. 1-34
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Journal article (peer-reviewed)abstract
- We introduce a path-based cyclic proof system for first-order mu-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal mu-calculus.
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| 6. |
- Ahmed, Chwas, et al.
(author)
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Tonal partition algebras : fundamental and geometrical aspects of representation theory
- 2024
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In: Communications in Algebra. - : Taylor & Francis. - 0092-7872 .- 1532-4125. ; 52:1, s. 233-271
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Journal article (peer-reviewed)abstract
- For l, n is an element of N we define tonal partition algebra P-l (n) over Z[delta]. We construct modules {Delta mu} mu for P-l (n) over Z[delta], and hence over any integral domain containing Z[delta] (such as C[delta]), that pass to a complete set of irreducible modules over the field of fractions. We show that P-l (n) is semisimple there. That is, we construct for the tonal partition algebras a modular system in the sense of Brauer. Using a "geometrical" index set for the Delta-modules, we give an order with respect to which the decomposition matrix over C (with d. C-x) is upper-unitriangular. We establish several crucial properties of the Delta-modules. These include a tower property, with respect to n, in the sense of Green and Cox-Martin-Parker-Xi; contravariant forms with respect to a natural involutive antiautomorphism; a highest weight category property; and branching rules.
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| 7. |
- Alper, Jarod, et al.
(author)
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Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts
- 2024
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In: Forum of Mathematics, Sigma. - : Cambridge University Press (CUP). - 2050-5094. ; 12
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Journal article (peer-reviewed)abstract
- We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of étale, smooth or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove local structure theorems for stacks and their derived counterparts and the existence of henselizations along linearly fundamental closed substacks. These results establish the existence of Ferrand pushouts, which answers positively a question of Temkin-Tyomkin.
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| 8. |
- Alsaody, Seidon
(author)
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Groups of type E6 and E7 over rings via Brown algebras and related torsors
- 2024
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In: Journal of Algebra. - : Elsevier. - 0021-8693 .- 1090-266X. ; 656, s. 24-46
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Journal article (peer-reviewed)abstract
- We study structurable algebras and their associated Freudenthal triple systems over commutative rings. The automorphism groups of these triple systems are exceptional groups of type E 7 , and we realize groups of type E 6 as centralizers. When 6 is invertible, we further give a geometric description of homogeneous spaces of type E 7 / E 6 , and show that they parametrize principal isotopes of Brown algebras. As opposed to the situation over fields, we show that such isotopes may be non-isomorphic. (c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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| 9. |
- Baeza-Ballesteros, Jorge, et al.
(author)
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The three-pion K-matrix at NLO in ChPT
- 2024
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In: Journal of High Energy Physics. - 1029-8479. ; 2024:3
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Journal article (peer-reviewed)abstract
- The three-particle K-matrix, Kdf,3, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.
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| 10. |
- Bagio, Dirceu, et al.
(author)
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The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- 2024
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In: Forum mathematicum. - : Walter de Gruyter. - 0933-7741 .- 1435-5337.
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Journal article (peer-reviewed)abstract
- Given a partial action α of a groupoid G on a ring R, we study the associated partial skew groupoid ring R ⋊ α G {R\rtimes_{\alpha}G}, which carries a natural G-grading. We show that there is a one-to-one correspondence between the G-invariant ideals of R and the graded ideals of the G-graded ring R ⋊ α G {R\rtimes_{\alpha}G}. We provide sufficient conditions for primeness, and necessary and sufficient conditions for simplicity of R ⋊ α G {R\rtimes_{\alpha}G}. We show that every ideal of R ⋊ α G {R\rtimes_{\alpha}G} is graded if and only if α has the residual intersection property. Furthermore, if α is induced by a topological partial action θ, then we prove that minimality of θ is equivalent to G-simplicity of R, topological transitivity of θ is equivalent to G-primeness of R, and topological freeness of θ on every closed invariant subset of the underlying topological space is equivalent to α having the residual intersection property. As an application, we characterize condition (K) for an ultragraph in terms of topological properties of the associated partial action and in terms of algebraic properties of the associated ultragraph algebra. © 2024 Walter de Gruyter GmbH, Berlin/Boston 2024.
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