Inspired by the study of vertex operator algebra extensions, we answer the question of when
the category of local modules over a commutative exact algebra in a braided finite tensor …

In this paper we construct “structural” pre-braidings characterizing different algebraic
structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some …

We study solvability, nilpotency and splitting property for algebraic supergroups over an
arbitrary field K of characteristic char K≠ 2. Our first main theorem tells us that an algebraic …

The determination of cyclic (co) homology of a given algebra is a quite important and difficult
problem. Let us briefly recall some of the results obtained that are somehow related to our …

The natural problem we approach in the present paper is to show how the notion of formally
smooth (co) algebra inside monoidal categories can substitute that of (co) separable (co) …

The main goal of this paper is to investigate the structure of Hopf algebras with the property
that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. Let us …

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We show that for a braided Hopf algebra in the category of comodules over a cosemisimple
coquasitriangular Hopf algebra, the Hochschild cohomological dimension, the left and right …

To every dual quasi-bialgebra H and every bialgebra R in the category of Yetter–Drinfeld
modules over H, one can associate a dual quasi-bialgebra, called bosonization. In this …

In this paper monoidal Hom-Lie algebras, Lie color algebras, Lie superalgebras and other
type of generalized Lie algebras are recovered by means of an iterated construction, known …