For a smooth manifold equipped with a compact Lie group action, we construct an equivariant cohomology theory which takes values in a vertex algebra, and contains the classical equivariant cohomology as a subalgebra. The main idea is to synthesize the algebraic approach to the classical equivariant cohomology theory due to H. Cartan and Guillemin-Sternberg, with the chiral de Rham algebra of Ma...

A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The scheme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated by a Cartan subalgebra and generally exist in su(N). In particular, the Lie algebras su(2) and every su(2 < N < 2p) share the isomorphic structure of the q...

For a smooth manifold equipped with a compact Lie group action, we construct an equivariant cohomology theory which takes values in a vertex algebra, and contains the classical equivariant cohomology as a subalgebra. The main idea is to synthesize the algebraic approach to the classical equivariant cohomology theory due to H. Cartan and Guillemin-Sternberg, with the chiral de Rham algebra of Ma...

Let Uq(sl2) be the quantized enveloping algebra associated to the simple Lie algebra sl2. In this paper, we study the quantum double Dq of the Borel subalgebra Uq((sl2) ) of Uq(sl2). We construct an analogue of Kostant–Lusztig Z[v, v]-form for Dq and show that it is a Hopf subalgebra. We prove that, over an algebraically closed field, every simple Dq-module is the pullback of a simple Uq(sl2)-m...

We associate to an arbitrary positive root [Formula: see text] of a complex semisimple finite-dimensional Lie algebra twisting endofunctor the category text]-modules. apply this functor generalized Verma modules in and construct family text]-Gelfand–Tsetlin with finite text]-multiplicities, where is commutative text]-subalgebra universal enveloping generated by Cartan subalgebra Casimir element...

In this paper, a class of non-weight modules over the topological N = 2 super-BMS3 algebra g are completely constructed. Assume that h̄=CL0⊕CP0⊕CG0⊕CQ0 is Cartan subalgebra and h=CL0⊕CP0 two-dimensional h̄. These free rank as h. fact, these reducible. Moreover, we give complete classification U(h)-modules g.