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pro vyhledávání: '"17a60"'
Leibniz algebras are non skew-symmetric generalization of Lie algebras. In this paper we introduce the notion of anti-Leibniz algebras as a "non commutative version" of mock-Lie algebras. Low dimensional classification of such algebras is given. Then
Externí odkaz:
http://arxiv.org/abs/2409.17184
Publikováno v:
Journal of Algebra (2025) 663: 210-258
It is known that the operads of perm algebras and pre-Lie algebras are the Koszul dual each other and hence there is a Lie algebra structure on the tensor product of a perm algebra and a pre-Lie algebra. Conversely, we construct a special perm algebr
Externí odkaz:
http://arxiv.org/abs/2409.13230
Autor:
Casado, Yolanda Cabrera, Gonçalves, María Inez Cardoso, Gonçalves, Daniel, Barquero, Dolores Martín, González, Cándido Martín, Campos, Iván Ruiz
In this paper, we establish a connection between evolution algebras of dimension two and Hopf algebras, via the algebraic group of automorphisms of an evolution algebra. Initially, we describe the Hopf algebra associated with the automorphism group o
Externí odkaz:
http://arxiv.org/abs/2407.15769
Autor:
Bahturin, Yuri, Olshanskii, Alexander
We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields. The notion o
Externí odkaz:
http://arxiv.org/abs/2406.15631
The construction of Sweedler duality is an important tool in the theory of Hopf algebras over a field, which is a right adjoint to the dual algebra functor. In this paper, we study the Sweedler duality of Hom-algebras and their Hom-modules. We delve
Externí odkaz:
http://arxiv.org/abs/2405.11838
Autor:
Manoharmayum, Jayanta
This paper studies nonassociative filtered rings using associated gradations. We show that a complete filtered ring $R$ with affine associated graded ring generated in degree $1$ is a local ring, and prove that the Artin--Rees lemma holds for $R$. As
Externí odkaz:
http://arxiv.org/abs/2401.17508
Autor:
Feldvoss, Jörg
The goal of this paper is to describe the structure of finite-dimensional semi-simple Leibniz algebras in characteristic zero. Our main tool in this endeavor are hemi-semidirect products. One of the major results of this paper is a simplicity criteri
Externí odkaz:
http://arxiv.org/abs/2401.05588
The main purpose of this paper is to introduce and investigate the notion of Jacobi-Jordan conformal algebra. They are a generalization of Jacobi-Jordan algebras which correspond to the case in which the formal parameter lambda equals 0. We consider
Externí odkaz:
http://arxiv.org/abs/2401.02206
For any set S, the free magmatic algebra spanned by card(S) binary products is the vector space spanned by the set of all planar rooted binary trees with the internal nodes colored by the elements of S, graded by the number of leaves of a tree. We sh
Externí odkaz:
http://arxiv.org/abs/2401.01890
Autor:
Towers, David A.
This paper starts by showing that for algebras in a certain class the concepts of weak nilpotency and nilpotency coincide. It goes on to describe some solvability and nilpotency properties of bicommutative algebras, of assosymmetric and of Novikov al
Externí odkaz:
http://arxiv.org/abs/2312.13113