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Sutlu S - One of the best experts on this subject based on the ideXlab platform.
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Hom-Lie-Hopf algebras
'Elsevier BV', 2020Co-Authors: Halici S, Karatas A, Sutlu SAbstract:We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (alpha, beta)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (alpha, Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras. (C) 2020 Elsevier Inc. All rights reserved.C1 [Halici, S.; Karatas, A.] Pamukkale Univ, Denizli, Turkey.[Sutlu, S.] Isik Univ, Istanbul, Turkey
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Hom-Lie-Hopf algebras
'Elsevier BV', 2020Co-Authors: Halici S, Karatas A, Sutlu SAbstract:We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras. © 2020 Elsevier Inc
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Hom-Lie-Hopf algebras
2019Co-Authors: Halici S, Karatas A, Sutlu SAbstract:We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general $(\alpha,\beta)$-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of $(\alpha,{\rm Id})$-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras
Lamei Yuan - One of the best experts on this subject based on the ideXlab platform.
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hom lie color algebra structures
Communications in Algebra, 2012Co-Authors: Lamei YuanAbstract:The aim of this article is to introduce the notion of Hom-Lie color algebras. This class of algebras is a natural generalization of the Hom-Lie algebras as well as a special case of the quasi-hom-Lie algebras. In the article, homomorphism relations between Hom-Lie color algebras are defined and studied. We present a way to obtain Hom-Lie color algebras from the classical Lie color algebras along with algebra endomorphisms and offer some applications. Also, we introduce a multiplier σ on the abelian group Γ and provide constructions of new Hom-Lie color algebras from old ones by the σ-twists. Finally, we explore some general classes of Hom-Lie color admissible algebras and describe all these classes via G–Hom-associative color algebras, where G is a subgroup of the symmetric group S 3.
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hom lie color algebra structures
arXiv: Rings and Algebras, 2010Co-Authors: Lamei YuanAbstract:This paper introduces the notion of Hom-Lie color algebra, which is a natural general- ization of Hom-Lie (super)algebras. Hom-Lie color algebras include also as special cases Lie (super) algebras and Lie color algebras. We study the homomorphism relation of Hom-Lie color algebras, and construct new algebras of such kind by a \sigma-twist. Hom-Lie color admissible algebras are also defined and investigated. They are finally classified via G-Hom-associative color algebras, where G is a subgroup of the symmetric group S_3.
Hiromichi Yamada - One of the best experts on this subject based on the ideXlab platform.
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zhu s algebra c2 algebra and c2 cofiniteness of parafermion vertex operator algebras
Advances in Mathematics, 2014Co-Authors: Tomoyuki Arakawa, Ching Hung Lam, Hiromichi YamadaAbstract:Abstract We study Zhu's algebra, C 2 -algebra and C 2 -cofiniteness of parafermion vertex operator algebras. We first give a detailed study of Zhu's algebra and C 2 -algebra of parafermion vertex operator algebras associated with the affine Kac–Moody Lie algebra s l ˆ 2 . We show that they have the same dimension and Zhu's algebra is semisimple. The classification of irreducible modules is also established. Finally, we prove that the parafermion vertex operator algebras for any finite dimensional simple Lie algebras are C 2 -cofinite.
Sergio Arturo Celani - One of the best experts on this subject based on the ideXlab platform.
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priestley dualities for some lattice ordered algebraic structures including mtl imtl and mv algebras
Open Mathematics, 2006Co-Authors: Leonardo Manuel Cabrer, Sergio Arturo CelaniAbstract:In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 5). These dualities are obtained by restricting the duality given by the second author for DLFI- algebras by means of Priestley spaces with ternary relations (see (2)). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space. c
Halici S - One of the best experts on this subject based on the ideXlab platform.
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Hom-Lie-Hopf algebras
'Elsevier BV', 2020Co-Authors: Halici S, Karatas A, Sutlu SAbstract:We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (alpha, beta)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (alpha, Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras. (C) 2020 Elsevier Inc. All rights reserved.C1 [Halici, S.; Karatas, A.] Pamukkale Univ, Denizli, Turkey.[Sutlu, S.] Isik Univ, Istanbul, Turkey
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Hom-Lie-Hopf algebras
'Elsevier BV', 2020Co-Authors: Halici S, Karatas A, Sutlu SAbstract:We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras. © 2020 Elsevier Inc
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Hom-Lie-Hopf algebras
2019Co-Authors: Halici S, Karatas A, Sutlu SAbstract:We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general $(\alpha,\beta)$-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of $(\alpha,{\rm Id})$-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras
