Algebra structures onhom(C,L)

L∞ algebra structures of Lie algebra deformations

In this paper,we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into Strong homotopy Lie algebra or L∞ algebra. All such obstructions have been transfered to the revelvant L∞ algebras which contain only three terms.

Hom-algebra structures

A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov in [4] and extended by Larsson and Silvestrov to quasi-hom Lie and quasi-Lie algebras in [5, 6]. In this paper we introduce and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic struc...

Kernels over Relational Algebra Structures

In this paper we present a novel and general framework based on concepts of relational algebra for kernel-based learning over relational schema. We exploit the notion of foreign keys to define a new attribute that we call instanceset and we use this type of attributes to define a tree like structured representation of the learning instances. We define kernel functions over relational schemata w...

PostLie algebra structures on the Lie Algebra SL(2,Ca)

Yang – Baxter Operators from Algebra Structures and Lie Super - Algebra Structures

The concept of symmetry plays an important role in solving equations and systems of equations. We will present solutions for the (constant and spectral-parameter) Yang-Baxter equations and Yang-Baxter systems arising from algebra structures and discuss about their symmetries. In the last section, we present enhanced versions of Theorem 1 (from [20]), solutions for the classical Yang-Baxter equa...