Related papers: Quantized enveloping superalgebra of type $P$
We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory for periplectic Lie superalgebras. We determine when the algebra is quasi-hereditary and, for fields of characteristic zero, describe the block…
We study some elementary properties of the quantum enveloping algebra associated to a parabolic subalgebra $\mathfrak{p}$ of a semisimple Lie algebra $\mathfrak{g}$. In particular we prove an explicit formula for the degree of this algebra,…
We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…
The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping…
We exhibit a PI Hopf algebra that is not a finite module over its center. We survey some ring-theoretical properties of the bosonizations of enveloping algebras of Lie superalgebras.
We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q -> 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed…
Suppose $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1} is a Lie superalgebra of queer type or periplectic type over an algebraically closed field $\textbf{k}$ of characteristic $p>2$. In this article, we initiate preliminarily to…
We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric…
We introduce an integral form U of the quantized enveloping algebra of sl_2. The algebra U is just large enough so that the quasi-R-matrix is contained in a completion of U\otimes U. We study several completions of the algebra U, and…
Degenerating the quantum queer Schur superalgebra ${\mathcal{Q}_q(n,r; R)}$ to the case $q=1$, the queer Schur superalgebra ${\mathcal{Q}(n,r)}$ is obtained. In this article, we reconstruct the universal enveloping algebra…
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined in this context. An extension to the…
We introduce the notion of $\imath$Schur superalgebra, which can be regarded as a type B/C counterpart of the $q$-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed $q$-permutation modules over Hecke…
In this paper, we define and study the universal enveloping algebra of a Poisson superalgebra. In particular, a new PBW Theorem for Lie-Rinehart superalgebras is proved leading to a PBW Theorem for Poisson superalgebras, we show the…
In this article, the two-parameter quantum Heisenberg enveloping algebra, which serves as a model for certain quantum generalized Heisenberg algebras, have been studied at roots of unity. In this context, the quantum Heisenberg enveloping…
As a natural generalization quantum Schur algebras associated with the Hecke algebra of the symmetric group, we introduce the quantum Schur superalgebra of type Q associated with the Hecke-Clifford superalgebra, which, by definition, is the…
By using cocycle deformation, we construct a certain class of Hopf algebras, containing the quantized enveloping algebras and their analogues, from what we call pre-Nichols algebras. Our construction generalizes in some sense the known…
We introduce a new algebra B_l(z,q) depending on two nonzero complex parameters such that B_l(q^n,q) at q=1 coincides with the Brauer algebra B_l(n). We establish an analog of the Brauer-Schur-Weyl duality where the action of the new…
The generalized Cartan type $\mathbf{S}$ Lie algebras in char 0 with the Lie bialgebra structures involved are quantized, where the Drinfel'd twist we used is proved to be a variation of the Jordanian twist. As the passage from char 0 to…
We obtain a presentation of quantum Schur algebras (over the field Q(v)) by generators and relations. This presentation is compatible with the usual presentation of the quantized universal enveloping algebra of the Lie algebra gl(2). We…
The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…