Related papers: Lie Algebras in Fock Space

We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebras, as well as a classification in three and…

We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable…

This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…

In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…

An analogue of Serre's theorem is established for finite dimensional simple Lie superalgebras, which describes presentations in terms of Chevalley generators and Serre type relations relative to all possible choices of Borel subalgebras.…

We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.

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),…

Dynkin's classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to Lie subsuperalgebras of the general linear Lie superalgebras.

In this article we introduce a generalization of the Khovanov--Lauda Rouquier algebras, the electric KLR algebras. These are superalgebras which connect to super Brauer algebras in the same way as ordinary KLR-algebras of type $A$ connect…

For locally convex, nilpotent Lie algebras we construct faithful representations by nilpotent operators on a suitable locally convex space. In the special case of nilpotent Banach-Lie algebras we get norm continuous representations by…

This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.

Using adjoint representation of Lie superalgebras, we obtain the matrix form of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By direct calculations of these identities, and use of automorphism supergroups of two…

Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.

We describe the Fock space representations and crystal bases for the affine Kac-Moody Lie algebra of type $C_n^{(1)}$ in terms of coloured Young diagrams.

We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.

In this paper we consider the very wide class of varieties of representations of Lie algebras over the field k, which has characteristic 0. We study the relation between the geometric equivalence and automorphic equivalence of the…

We introduce invariant algebras and representation$^{(c_1,..., c_8)}$ of algebras, and give many ways of constructing Lie algebras, Jordan algebras, Leibniz algebras, pre-Lie algebras and left-symmetric algebras in an invariant algebras.

We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…

In this paper, we present a study on the prolongations of representations of Lie algebras. We show that a tangent bundle of a given Lie algebra attains a Lie algebra structure. Then, we prove that this tangent bundle is algebraically…

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…