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Double Hom-Associative Algebra and Double Hom–Lie Bialgebra

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0 Published in 2019 at "Advances in Applied Clifford Algebras"

DOI: 10.1007/s00006-019-1028-2

Abstract: Recently, Hom-structures have been widely investigated in literature. In this paper, we introduce the conceptions of double Hom-associative algebras and double Hom–Lie bialgebras, and give a necessary and sufficient condition for double Hom-associative algebras to… read more here.

Keywords: hom; hom lie; hom associative; associative algebras ... See more keywords

Hom-Lie algebroids and hom-left-symmetric algebroids

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0 Published in 2017 at "Journal of Geometry and Physics"

DOI: 10.1016/j.geomphys.2017.01.029

Abstract: Abstract We give a notion of hom-left-symmetric algebroids, which are a generalization of hom-left symmetric algebras. We construct several examples of hom-Lie algebroids and hom-left-symmetric algebroids. Representations of hom-Lie algebroids and hom-left-symmetric algebroids are given.… read more here.

Keywords: symmetric algebroids; hom lie; left symmetric; algebroids hom ... See more keywords

Hom-Lie structures on Kac–Moody algebras

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1 Published in 2018 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.08.022

Abstract: Abstract We describe Hom-Lie structures on affine Kac–Moody and related Lie algebras, and discuss the question when they form a Jordan algebra. read more here.

Keywords: hom lie; kac moody; lie structures; lie ... See more keywords

COMPLEX PRODUCT STRUCTURES ON HOM-LIE ALGEBRAS

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0 Published in 2018 at "Glasgow Mathematical Journal"

DOI: 10.1017/s001708951800006x

Abstract: Abstract In this paper, we introduce the notion of complex product structures on hom-Lie algebras and show that a hom-Lie algebra carrying a complex product structure is a double hom-Lie algebra and it is also… read more here.

Keywords: complex product; lie algebras; hom lie; product ... See more keywords

On parakähler Hom-Lie algebras and Hom-left-symmetric bialgebras

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0 Published in 2017 at "Communications in Algebra"

DOI: 10.1080/00927872.2016.1175453

Abstract: ABSTRACT In this paper, the parakähler Hom-Lie algebras or phase space of Hom-Lie algebras in terms of Hom-left-symmetric algebras are studied. A structure theory of parakähler Hom-Lie algebras in terms of matched pairs of Hom-Lie… read more here.

Keywords: hom; lie algebras; hom lie; left symmetric ... See more keywords

On Hom-Lie superbialgebras

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0 Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1468900

Abstract: Abstract The purpose of this paper is to generalize to -graded case the study of Hom-Lie bialgebras which were discussed first by D. Yau, then by Y. Sheng and C. Bai. We first provide various… read more here.

Keywords: hom lie; lie superbialgebras;

Geometric aspects of extensions of hom-Lie superalgebras

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0 Published in 2017 at "International Journal of Geometric Methods in Modern Physics"

DOI: 10.1142/s0219887817500852

Abstract: In this paper, we deal with (non-abelian) extensions of a given hom-Lie superalgebra and find a cohomological obstacle to the existence of extensions of hom-Lie superalgebras. Moreover, the setting of covariant exterior derivatives, super connection,… read more here.

Keywords: lie superalgebras; hom lie; geometric aspects; aspects extensions ... See more keywords

Hom-Lie group and hom-Lie algebra from Lie group and Lie algebra perspective

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1 Published in 2021 at "International Journal of Geometric Methods in Modern Physics"

DOI: 10.1142/s0219887821500687

Abstract: A hom-Lie group structure is a smooth group-like multiplication on a manifold, where the structure is twisted by a isomorphism. The notion of hom-Lie group was introduced by Jiang et al. as integra... read more here.

Keywords: lie algebra; hom lie; group hom; group ... See more keywords

Equivalent Description of Hom-Lie Algebroids

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0 Published in 2018 at "Advances in Mathematical Physics"

DOI: 10.1155/2018/8417516

Abstract: We study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids, and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be transformed into each other… read more here.

Keywords: lie algebroids; hom lie; description hom; equivalent description ... See more keywords

Representations and Deformations of Hom-Lie-Yamaguti Superalgebras

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0 Published in 2020 at "Advances in Mathematical Physics"

DOI: 10.1155/2020/9876738

Abstract: Let L,α be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Also, we introduce the notions of generalized derivations and representations of L,α and present some properties. Finally, we… read more here.

Keywords: lie yamaguti; representations deformations; yamaguti superalgebras; hom lie ... See more keywords

Extensions of hom-Lie color algebras

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1 Published in 2019 at "Georgian Mathematical Journal"

DOI: 10.1515/gmj-2019-2033

Abstract: 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{\mathfrak{g}} by another… read more here.

Keywords: extensions hom; lie color; hom lie; color algebra ... See more keywords