Based on the NilHecke algebra $\mathsf{NH}_n$, odd developed by Ellis, Khovanov and Lauda Kang, Kashiwara Tsuchioka's quiver Hecke superalgebra, we develop Clifford superalgebra $\mathsf{NH}\mathfrak{C}_n$ as another super-algebraic analogue of $\mathsf{NH}_n$. We show that there is a notion symmetric polynomials fitting in this picture, prove these are generated an appropriate elementary polyn...

We describe the unconventional infinite-dimensional Hopf superalgebra related to the integrable S-matrix of the AdS/CFT correspondence, and discuss its typical and atypical representations.

As a natural generalisation of q-Schur algebras associated with the Hecke algebra Hr,R (of the symmetric group), we introduce the Q-q-Schur superalgebra associated with the Hecke-Clifford superalgebra H r,R, which, by definition, is the endomorphism algebra of the induced H r,R-module from certain q-permutation modules over Hr,R. We will describe certain integral bases for these superalgebras i...

In this paper, we classify the compatible left-symmetric superalgebra structures on the super-Virasoro algebras satisfying certain natural conditions.

A Lie superalgebra is called quasi-Frobenius if it admits a closed anti-symmetric non-degenerate bilinear form. We study the notion of double extensions when form either orthosymplectic or periplectic. show that every satisfies certain conditions can be obtained as extension smaller superalgebra. classify all 4-dimensional superalgebras, and such superalgebras must solvable. [Formula: see text]...

We present and prove in detail a Poincaré–Birkhoff–Witt commutator lemma for the quantum superalgebra Uq[gl(m|n)].

A Gel’fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1, 0, . ....

In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is...