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.

Abstract We contribute to the study of Rota–Baxter operators on types algebras other than associative and Lie algebras. If A is an algebra a certain type R operator , one can define new multiplication by means previous ask under what circumstances same as . Our first main result deals with such situation in case BiHom-Lie second BiHom analogue Aguiar’s theorem that shows how obtain pre-Lie from...

Characterization of the *-subalgebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are given. These conditions are generalization of the unshrinkability of monomial *-algebras introduced by C. Lance and P. Tapper. The applications t...

We compute the Hochschild homology and cohomology, and cyclic homology, of almost Calabi-Yau algebras for SU(3) ADE graphs. These almost Calabi-Yau algebras are a higher rank analogue of the pre-projective algebras for Dynkin diagrams, which are SU(2)-related constructions. The Hochschild (co)homology and cyclic homology of A can be regarded as invariants for the braided subfactors associated t...

EQ-algebras were introduced by Novak (2006) as an algebraic structure of truth values for fuzzy-type theory (FFT). Novák and De Baets (2009) various kinds such good, residuated, IEQ-algebras. In this paper, we define the notion (pre)ideal in bounded (BEQ-algebras) investigate some properties. Then, introduce a congruence relation on good BEQ-algebras using ideals, then, solve open problem Paad ...

We introduce two chains of unary operations in the MVn algebra of Revaz Grigolia; they will be used in establishing many connections between these algebras and n-valued Lukasiewicz-Moisil algebras (LMn algebras for short). The study has four parts. It is by and large self-contained. The main result of the rst part is that MV4 algebras coincide with LM4 algebras. The larger class of \relaxed"-MV...

In this article we prove that there exists an explicit bijection between nice $d$-pre-Calabi-Yau algebras and $d$-double Poisson differential graded algebras, where $d \in \mathbb{Z}$, extending a result proved by N. Iyudu M. Kontsevich. We also show correspondence is functorial in quite satisfactory way, giving rise to (partial) functor from the category of dg partial algebras. Finally, furthe...

In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter ( RB $\mathsf {RB}$ ) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L ∞ $L_\infty$ -algebra whose Maurer–Cartan elements are algebras. Then using the twisting method, that controls deformations a algebra. Meanwhile, cohomolo...