Recently, relative Rota–Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider Leibniz (rRB algebras) as object our study. We construct an L∞-algebra that characterizes rRB its Maurer–Cartan elements. Then define representations algebra and introduce cohomology with coefficients a representation. As applications ...

In this paper, we consider Leibniz algebras with derivations. A pair consisting of a algebra and distinguished derivation is called LeibDer pair. We define cohomology theory for coefficients in representation. study central extensions the next, generalize formal deformation to pairs which deform both bracket derivation. It governed by itself. Finally, homotopy derivations on sh 2-derivations 2-...

We set up a fibred categorical theory of obstruction and classification morphisms that specialises to the one monoidal functors between groups also Schreier-Mac Lane group extensions. Further applications are provided crossed extensions bimodule butterflies, with in particular non-abelian unital associative algebras terms Hochschild cohomology.

Recently, a number of new classes of infinite-dimensional simple Lie algebras over a Field of characteristic 0 were discovered by several authors (see the references at the end of this paper). Among those algebras, are the generalized Witt algebras. The higher rank Virasoro algebras was introduced by Patera and Zassenhaus [PZ], which are 1-dimensional universal central extensions of some genera...

This paper concerns classifying completely positive maps between certain C*-algebras. Several invariants for are constructed. It is proved that one of them isomorphic to the Ext-group C*-algebra extensions in special circumstances. Furthermore, this invariant induces a functor from C*-algebras abelian groups which split-exact.

Abstract It is well known that classical varieties of $\Sigma$ -algebras correspond bijectively to finitary monads on $\mathsf{Set}$ . We present an analogous result for ordered -algebras, is, categories algebras presented by inequations between -terms. prove they strongly $\mathsf{Pos}$ That those which preserve reflexive coinserters. deduce have a coinserter presentation, the coequalizer pres...

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...