Let L be a finitely generated free color Lie superalgebra. We obtain new almost primitive and test elements of L. AMS Subject Classification: 17B01, 17B40

We describe the centre of a simple Lie superalgebra of type P (n). The description is based on the notion of anticentre.

Para-Fermi statistics and Fermi statistics are known to be associated with particular representations of the Lie algebra so(2n+1)≡ Bn. Similarly paraBose and Bose statistics are related with the Lie superalgebra osp(1|2n)≡ B(0|n). We develop an algebraical framework for the generalization of quantum statistics based on the Lie algebras An, Bn, Cn and Dn.

Some locally finite simple Lie algebras are graded by finite (possibly nonreduced) root systems. Many more algebras are sufficiently close to being root graded that they still can be handled by the techniques from that area. In this paper we single out such Lie algebras, describe them, and suggest some applications of such descriptions.

Let V be a finite-dimensional superspace over C and g a simple (or a “close” to simple) matrix Lie superalgebra, i.e., a Lie subsuperalgebra in gl(V ). Under the classical invariant theory for g we mean the description of g-invariant elements of the algebra A p,q k,l = S . (V k ⊕Π(V ) ⊕ V ∗p ⊕Π(V )). We give such description for gl(V ), sl(V ) and osp(V ) and their “odd” analogs: q(V ), sq(V );...

We present explicit free field representations for the N = 4 doubly extended superconformal algebra, Ãγ. This algebra generalizes and contains all previous N = 4 superconformal algebras. We have found Ãγ to be obtained by hamiltonian reduction of the Lie superalgebra D(2|1;α). In addition, screening operators are explicitly given and the associated singular vectors identified. We use this to pr...

The enveloping algebra U(g) of the Lie superalgebra g has a deformation, called the Yangian of qN . For each M = 1 ,2 , . . . denote by A M N the centralizer of qM ⊂ qN+M in the associative superalgebra U(qN+M ) . We construct a sequence of surjective homomorphisms U(qN ) ← A 1 N ← A 2 N ← . . . . We describe the inverse limit of the sequence of centralizer algebras A1N ,A 2 N , . . . in terms ...

The generalized quantum group U(ϵ) of type A is an affine analogue associated to a general linear Lie superalgebra glM|N. We prove that there exists unique R matrix on the tensor product fundamental representations for arbitrary parameter sequence ϵ corresponding non-conjugate Borel subalgebra give explicit description its spectral decomposition, and then as application, construct family finite...