189 research outputs found
Quasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities
This paper begins by introducing the concept of a quasi-hom-Lie algebra which
is a natural generalization of hom-Lie algebras introduced in a previous paper
by the authors. Quasi-hom-Lie algebras include also as special cases (color)
Lie algebras and superalgebras, and can be seen as deformations of these by
homomorphisms, twisting the Jacobi identity and skew-symmetry. The natural
realm for these quasi-hom-Lie algebras is as a generalization-deformation of
the Witt algebra \Witt of derivations on the Laurent polynomials
\C[t,t^{-1}]. We also develop a theory of central extensions for qhl-algebras
which can be used to deform and generalize the Virasoro algebra by centrally
extending the deformed Witt type algebras constructed here. In addition, we
give a number of other interesting examples of quasi-hom-Lie algebras, among
them a deformation of the loop algebra.Comment: 40 page
Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras
The aim of this paper is to generalize the concept of Lie-admissible
coalgebra introduced by Goze and Remm to Hom-coalgebras and to introduce
Hom-Hopf algebras with some properties. These structures are based on the
Hom-algebra structures introduced by the authors.Comment: 13 page
Commutativity and ideals in algebraic crossed products
We investigate properties of commutative subrings and ideals in
non-commutative algebraic crossed products for actions by arbitrary groups. A
description of the commutant of the base coefficient subring in the crossed
product ring is given. Conditions for commutativity and maximal commutativity
of the commutant of the base subring are provided in terms of the action as
well as in terms of the intersection of ideals in the crossed product ring with
the base subring, specially taking into account both the case of base rings
without non-trivial zero-divisors and the case of base rings with non-trivial
zero-divisors
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