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On Nichols algebras over basic Hopf algebras
(Springer, 2020-12-02)
This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field k of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is ...
The Lie algebra of derivations of a current Lie algebra
(Taylor & Francis, 2019-09)
Let K be a field of characteristic zero, g be a finite dimensional K-Lie algebra and let A be a finite dimensional associative and commutative K-algebra with unit. We describe the structure of the Lie algebra of derivations ...
Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras
(Springer, 2011-07)
There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, Lp,k, on a given finite field F(pk), and conversely. There exists an interpretation Φ1 of the variety V(Lp,k) generated by ...
Homotopy classification of Leavitt path algebras
(Academic Press Inc Elsevier Science, 2020-03)
In this paper we address the classification problem for purely infinite simple Leavitt path algebras of finite graphs over a field ℓ. Each graph E has associated a Leavitt path ℓ-algebra L(E). There is an open question ...
Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra
(European Mathematical Society, 2021-12-07)
For each nonzero h ∈ F[x], where F is a field, let Ah be the unital associative algebra generated by elements x; y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, ...
On cyclic algebraic-geometry codes
(Cornell University, 2021-06)
In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group ...
On finite-dimensional copointed Hopf algebras over dihedral groups
(Elsevier Science, 2019-08)
We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k D m over a dihedral group D m , with m=4a≥12. ...
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
(Canadian Mathematical Soc, 2014-12)
We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field ...
DiffAlg: a Differential Algebra Package
(Mathematical Science Publ, 2019-03-04)
In this article we present DiffAlg.m2, a differential algebra package for Macaulay2. It can perform the following operations: wedge products and exterior differentials of differential forms, contraction and Lie derivatives ...
A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
(European Mathematical Society, 2017-02)
Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the ...