E-algebra is an algebra(푋;∗,1)of type (2,0)that satisfies the following axioms:(퐵E1) 푥∗푥=1, (퐵E2) 푥∗1=1, (퐵E3) 1∗푥=푥, and (퐵E4) 푥∗(푦∗푧)=푦∗(푥∗푧)for all푥,푦,푧∈푋.In this paper, notionof q-derivation in BE-algebra defined its properties are discussed. Finally, of fixed set kernel a identified based on their relation to subalgebraand elements.

Generators of multiparameter deformations U q;s 1 ,s 2 ,...,s n−1 (gl n) of the universal enveloping algebra U (gl n) are realized bilinearly by means of appropriately generalized form of anyonic oscillators (AOs). This modification takes into account the parameters s 1 , ..., s n−1 and yields usual AOs when all the s i are set equal to unity. 1. Introduction. Various aspects of quantum groups ...

We describe transposed Poisson algebra structures on Block Lie algebras B(q) and superalgebras S(q), where q is an arbitrary complex number. Specifically, we show that the are trivial whenever q∉Z, for each q∈Z there only one (up to isomorphism) non-trivial structure B(q). The superalgebra S(q) admits q≠0 two non-isomorphic q=0. As a consequence, new admit Hom-Lie found.

We introduce the notion of quantum Schur (or q-Schur) superalgebras. These algebras share certain nice properties with q-Schur algebras such as base change property, existence of canonical Z[v, v]-bases, and the duality relation with quantum matrix superalgebra A(m|n). We also construct a cellular Q(υ)-basis and determine its associated cells, called super-cells, in terms of a Robinson–Schenste...