| 1. |
- Ilwale, Kwalombota, 1980-
(författare)
-
Noncommutative Riemannian Geometry of Twisted Derivations
- 2023
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A twisted derivation is a generalized derivative satisfying a twisted version of the ordinary Leibniz rule for products. In particular, a (σ, τ )-derivation on an algebra A, is a derivation where Leibniz rule is twisted by two endomorphisms σ and τ on A. Such derivations play an important role in the theory of quantum groups, as well as in the context of discretized and deformed derivatives. In this thesis, we develop a (commutative and noncommutative) differential geometry based on (σ, τ )- derivations. To this end, we introduce the notion of (σ, τ )-algebra, consisting of an associative algebra together with a set of (σ, τ )-derivations, to construct connections satisfying a twisted Leibniz rule in analogy with (σ, τ )-derivations. We show that such connections always exist on projective modules and that it is possible to construct connections compatible with a hermitian form. To construct torsion and curvature of (σ, τ )-connections, we introduce the notion of (σ, τ )-Lie algebra and demonstrate that it is possible to construct a Levi-Civita (σ, τ )-connection. Having constructed the framework for studying (σ, τ)-connections, we demonstrate that the framework applied to commutative algebras can help to also give a good understanding of (σ, τ )-derivations on commutative algebras. In particular, we introduce a notion of symmetric (σ, τ )-derivations together with some regularity conditions. For example, we show that strongly regular (σ, τ )-derivations are always inner and there exist a symmetric (σ, τ )-connection on symmetric (σ, τ )- algebras. Finally, we introduce a (σ, τ)-Hochschild cohomology theory which in first degree captures the outer (σ, τ )-derivations of an associative algebra. Along the way, examples including both commutative and noncommutative algebras are presented to illustrate the novel concepts.
|
|
| 2. |
- Alekseev, Aleksandr, et al.
(författare)
-
On (σ,τ)-Derivations of Group Algebra as Category Characters
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 81-99
-
Konferensbidrag (refereegranskat)abstract
- For the space of (σ,τ)-derivations of the group algebra C[G] of a discrete countable group G, the decomposition theorem for the space of (σ,τ)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several corollaries and examples describing when all (σ,τ)-derivations are inner are obtained. Considered in details are cases of (σ,τ)-nilpotent groups and (σ,τ)-FC groups.
|
|
| 3. |
- Arfa, Anja, et al.
(författare)
-
Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 33-60
-
Konferensbidrag (refereegranskat)abstract
- Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz algebras.
|
|
| 4. |
- Armakan, Abdoreza, et al.
(författare)
-
Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 61-79
-
Konferensbidrag (refereegranskat)abstract
- In this paper, the representations of color hom-Lie algebras have been reviewed and the existence of a series of coboundary operators is demonstrated. Moreover, the notion of a color omni-hom-Lie algebra associated to a linear space and an even invertible linear map have been introduced. In addition, characterization method for regular color hom-Lie algebra structures on a linear space is examined and it is shown that the underlying algebraic structure of the color omni-hom-Lie algebra is a color hom-Leibniz a algebra.
|
|
| 5. |
- Attari Polsangi, Ahmad Reza, et al.
(författare)
-
Decomposition of Complete Color Hom-Lie Algebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 101-120
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we study some equivalent conditions for a color hom-Lie algebra to be a complete color hom-Lie algebra. In particular, we discuss the relationship between decomposition and completness for a color hom-Lie algebra. Moreover, we check some conditions that the set of αs -derivations of a color hom-Lie algebra to be complete and simply complete. Finally, we find some conditions in which the decomposition into hom-ideals of the complete multiplicative color hom-Lie algebras is unique up to order of hom-algebra.
|
|
| 6. |
- Bakayoko, Ibrahima, et al.
(författare)
-
Hom-Prealternative Superalgebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 121-145
-
Konferensbidrag (refereegranskat)abstract
- The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative superalgebras are studied. Bimodules over Hom-prealternative superalgebras are introduced, relations between bimodules over Hom-prealternative superalgebras and the bimodules of the corresponding Hom-alternative superalgebras are considered, and construction of bimodules over Hom-prealternative superalgebras by twisting is described.
|
|
| 7. |
- Dassoundo, Mafoya Landry, et al.
(författare)
-
Nearly Associative and Nearly Hom-Associative Algebras and Bialgebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 259-284
-
Konferensbidrag (refereegranskat)abstract
- Basic definitions and properties of nearly associative algebras are described. Nearly associative algebras are proved to be Lie-admissible algebras. Two-dimensional nearly associative algebras are classified, and main classes are derived. The bimodules, matched pairs and Manin triple of a nearly associative algebras are derived and their equivalence with nearly associative bialgebras is proved. Basic definitions and properties of nearly Hom-associative algebras are described. Related bimodules and matched pairs are given, and associated identities are established.
|
|
| 8. |
|
|
| 9. |
- Domingos, Celso Djinja, et al.
(författare)
-
Some algebraic properties of representations of polynomial covariance type commutation relations
- 2023
-
Ingår i: Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures - Foundations and Applications. - : Springer. - 9783031393341 ; , s. 379-417
-
Bokkapitel (refereegranskat)abstract
- In this work conditions for additivity property of representations of polynomial covariance commutation relations are derived for operator algebras. Some other properties that this kind of representations fulfill are described. A reduction degree of the polynomial property of representations of this kind of commutation relations is presented for operator algebras. Moreover, representations of polynomial covariance commutation relations are derived for linear operators acting on the space of bounded real infinite sequences lp.
|
|
| 10. |
- Farhangdoost, Mohammed Reza, et al.
(författare)
-
Simply Complete Hom-Lie Superalgebras and Decomposition of Complete Hom-Lie Superalgebras
- 2023
-
Ingår i: Advances in Applied Clifford Algebras. - : Birkhauser. - 0188-7009 .- 1661-4909. ; 33:2
-
Tidskriftsartikel (refereegranskat)abstract
- Complete hom-Lie superalgebras are considered and some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the relation between decomposition and completeness for a hom-Lie superalgebra is described. Moreover, some conditions that the linear space of αs-derivations of a hom-Lie superalgebra to be complete and simply complete are obtained.
|
|
