منابع مشابه
Lie-admissible Algebras and Operads
A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie...
متن کاملBinary Trees, Geometric Lie Algebras, and Operads
Let T be a binary tree. We put a total ordering on its nodes as follows. If p1 and p2 are two distinct nodes of T , then there are two unique paths γ1 and γ2 from the root r of T . We say p1 < p2 if p1 is an ancestor of p2, or if when γ1 and γ2 first diverge at a node qi, γ1 goes right and γ2 goes left. This total ordering is called the preorder on T . It induces a total ordering of the leaves ...
متن کاملHom-lie Admissible Hom-coalgebras and Hom-hopf Algebras
The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12].
متن کاملOperads, Algebras and Modules
There are many different types of algebra: associative, associative and commutative, Lie, Poisson, etc., etc. Each comes with an appropriate notion of a module. As is becoming more and more important in a variety of fields, it is often necessary to deal with algebras and modules of these sorts “up to homotopy”. I shall give a very partial overview, concentrating on algebra, but saying a little ...
متن کاملVertex operator algebras and operads
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, n-ary operations for all n greater than or equal to 0, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation show...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.10.015