Related papers: Howe Duality of Type P
We consider two families of finite-dimensional simple Lie superalgebras of Cartan type, denoted by HO and KO, over an algebraically closed field of characteristic p>3. Using the weight space decompositions and the principal gradings we…
The symmetric group S_n possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of S_n itself, coincide with the irreducible representations of a certain algebra A_n.…
This paper considers the multiplicative Hom-Lie superalgebra structures on infinite dimensional simple Lie superalgebras of vector fields with characteristic zero. The main result is that there is only the multiplicative Hom-Lie…
Based on invariant algebras, we introduce representations$^{6-th}$ of Lie algebras and representations$^{< 4-th>}$ of Leibniz algebras, give the extended P-B-W Theorems in the context of the new representations of Lie algebras and Leibniz…
In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…
In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…
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…
Para-Bose and para-Fermi statistics are known to be associated with representations of the Lie (super)algebras of class B. We develop a framework for the generalization of quantum statistics based on the Lie superalgebras A(m|n), B(m|n),…
We determine the Lie superalgebras that are graded by the root systems of the basic classical simple Lie superalgebras of type A$(m,n)$.
We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view. By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to…
In this paper, various polynomial representations of strange classical Lie superalgebras are investigated. It turns out that the representations for the algebras of type P are indecomposable, and we obtain the composition series of the…
We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The first approach allows us to establish a generalised version…
An A-infinity bialgebra of type (m,n) is a Hopf algebra H equipped with a "compatible" operation \omega : H^{\otimes m} \to H^{\otimes n} of positive degree. We determine the structure relations for A-infinity bialgebras of type (m,n) and…
We define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…
Let $\mathfrak{g}$ be a finite dimensional complex simple classical Lie superalgebra and $A$ be a commutative, associative algebra with unity over $\mathbb{C}$. In this paper we define an integral form for the universal enveloping algebra…
The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups…
We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showing that an arbitrary split regular Hom-Lie superalgebra…
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real…
In this paper, we give defining relations of the affine Lie superalgebras an and defining relations of a super-version of the Drinfeld[D]-Jimbo[J] affine quantized universal enveloping algebras. As a result, we can exactly define the affine…