| 1. |
- Armakan, Abdoreza, et al.
(författare)
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Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras
- 2023
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Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 61-79
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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.
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| 2. |
- Armakan, Abdoreza, et al.
(författare)
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Enveloping algebras of certain types of color hom-Lie algebras
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 - 9783030418502 ; , s. 257-284
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Bokkapitel (refereegranskat)abstract
- In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free hom-associative color algebra on a hom-module is described for a certain type of color hom-Lie algebras and is applied to obtain the universal enveloping algebra of those hom-Lie color algebras. Finally, this construction is applied to obtain the extension of the well-known Poincaré–Birkhoff–Witt theorem for Lie algebras to the enveloping algebra of the certain types of color hom-Lie algebra such that some power of the twisting map is the identity map.
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| 3. |
- Armakan, Abdoreza, et al.
(författare)
-
Enveloping algebras of color hom-Lie algebras
- 2019
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Ingår i: Turkish Journal of Mathematics. - : SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK. - 1300-0098 .- 1303-6149. ; 43:1, s. 316-339
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincare- Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
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| 4. |
- Armakan, Abdoreza, et al.
(författare)
-
Extensions of hom-Lie color algebras
- 2021
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Ingår i: Georgian Mathematical Journal. - : Walter de Gruyter. - 1072-947X .- 1572-9176. ; 28:1, s. 2019-2033
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie color algebra g by another hom-Lie color algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i.e., we show that in order to have an extendible hom-Lie color algebra, there should exist a trivial member of the third cohomology.
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