We prove that finite GK-dimensional pre-Nichols algebras of super and standard type are quotients the corresponding distinguished algebras, except when braiding matrix is A dimension braided vector space three. For these two exceptions we explicitly construct substitutes as central extensions by a polynomial ring in one variable. Via bosonization this gives new examples Hopf algebras.

There have been several timed extensions of ACP-style process algebras with successful termination. None of them, to our knowledge, are equationally conservative (ground-)extensions of ACP with successful termination. Here, we point out some design decisions which were the possible causes of this misfortune and by taking different decisions, we propose a spectrum of timed process algebras order...

It is known that the monoidal t-norm based logic (MTL) and many of its schematic extensions are decidable. The usual way how to prove decidability of some schematic extension of MTL is to show that the corresponding class of algebras of truth values has the finite model property (FMP) or the finite embeddability property (FEP). However this method does not work for the extensions whose correspo...

The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index a superalgebra not greater than 4 and describe two-generated algebras odd generated superalgebras. discuss identities mono binary Leibniz algebras. It proven each quadratic algebra 2-step nilpotent. Also, we study double extensions

A class of nonassociative algebras is investigated with mild relations induced from metagroup structures. Modules over are studied. For a modules algebras, their extensions and splitting scrutinized. this purpose tensor products investigated. Moreover, developed cohomology theory on them used.

We study Galois extensions M (co-)H ⊂ M for H-(co)module algebras M if H is a Frobenius Hopf algebroid. The relation between the action and coaction pictures is analogous to that found in Hopf-Galois theory for finite dimensional Hopf algebras over fields. So we obtain generalizations of various classical theorems of Kreimer-Takeuchi, Doi-Takeuchi and Cohen-FischmanMontgomery. We find that the ...

Dendriform algebras are certain splitting of associative and arise naturally from Rota-Baxter operators, shuffle planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology homotopy analogs. The an algebra splits the Hochschild algebra. next, introduce a more general notion oriented algebras. We develop theory for that closely related to extensions gov...

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p, q) of the Cartan series Al and the pseudo-unitary algebras u(p, q), are completely determined and classified for arbitrary p, q. In addition to the su(p, q) and u(p, q) algebras, whose second cohomology group is well known to be trivi...