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| 3. |
- Alekseev, Aleksandr, et al.
(author)
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On (σ,τ)-Derivations of Group Algebra as Category Characters
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 81-99
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Conference paper (peer-reviewed)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.
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| 4. |
- Arfa, Anja, et al.
(author)
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Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 33-60
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Conference paper (peer-reviewed)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.
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| 5. |
- Armakan, Abdoreza, et al.
(author)
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Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 61-79
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Conference paper (peer-reviewed)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.
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| 6. |
- Attari Polsangi, Ahmad Reza, et al.
(author)
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Decomposition of Complete Color Hom-Lie Algebras
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 101-120
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Conference paper (peer-reviewed)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.
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| 7. |
- Bakayoko, Ibrahima, et al.
(author)
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Hom-Prealternative Superalgebras
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 121-145
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Conference paper (peer-reviewed)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.
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| 8. |
- Dassoundo, Mafoya Landry, et al.
(author)
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Nearly Associative and Nearly Hom-Associative Algebras and Bialgebras
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 259-284
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Conference paper (peer-reviewed)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.
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| 9. |
- García Butenegro, German, et al.
(author)
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Divisibility in Hom-Algebras, Single-Element Properties in Non-associative Algebras and Twisted Derivations
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 303-337
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Conference paper (peer-reviewed)abstract
- We compare and examine the influence of Hom-associativity, involving a linear map twisting the associativity axiom, on fundamental aspects important in study of Hom-algebras and (σ,τ)-derivations satisfying a (σ,τ)-twisted Leibniz product rule in connection to Hom-algebra structures. As divisibility may be not transitive in general not necessarily associative algebras, we explore factorization properties of elements in Hom-associative algebras, specially related to zero divisors, and develop an α-deformed divisibility sequence, formulated in terms of linear operators. We explore effects of the twisting maps σ and τ on the whole space of twisted derivations, unfold some partial results on the structure of (σ,τ)-derivations on arbitrary algebras based on a pivot element related to σ and τ and examine how general an algebra can be while preserving certain well-known relations between (σ,τ)-derivations. Furthermore, new more general axioms of Hom-associativity, Hom-alternativity and Hom-flexibility modulo kernel of a derivation are introduced leading to new classes of Hom-algebras motivated by (σ,τ)-Leibniz rule over multiplicative maps σ and τ and study of twisted derivations in arbitrary algebras and their connections to Hom-algebra structures.
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| 10. |
- García Butenegro, German, et al.
(author)
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On Lie-Type Constructions over Twisted Derivations
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 339-380
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Conference paper (peer-reviewed)abstract
- In this paper we examine interactions between (σ, τ) -derivations via commutator and consider new n-ary structures based on twisted derivation operators. We show that the sums of linear spaces of (σk, τl) -derivations and also of some of their subspaces, consisting of twisted derivations with some commutation relations with σ and τ, form Lie algebras, and moreover with the semigroup or group graded commutator product, yielding graded Lie algebras when the sum of the subspaces is direct. Furthermore, we extend these constructions of such Lie subalgebras spanned by twisted derivations of algebras to twisted derivations of n-ary algebras. Finally, we consider n-ary products defined by generalized Jacobian determinants based on (σ,τ) -derivations, and construct n-Hom-Lie algebras associated to the generalized Jacobian determinants based on twisted derivations extending some results of Filippov to (σ,τ) -derivations. We also establish commutation relations conditions for twisting maps and twisted derivations such that the generalised Jacobian determinant products yield (σ,τ,n) -Hom-Lie algebras, a new type of n-ary Hom-algebras different from n-Hom-Lie algebras in that the positions of twisting maps σ and τ are not fixed to positions of variables in n-ary products terms of the sum of defining identity as they were in Hom-Nambu-Filippov identity of n-Hom-Lie algebras.
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