Share

# Operator algebras, unitary representations, enveloping algebras, and invariant theory actes du colloque en l"honneur de Jacques Dixmier

• ·

Written in English

### Subjects:

• Lie groups -- Congresses.,
• Lie algebras -- Congresses.,
• Operator algebras -- Congresses.,
• Invariants -- Congresses.

## Book details:

Edition Notes

Classifications The Physical Object Statement edited by Alain Connes ... [et al.]. Series Progress in mathematics ;, v. 92, Progress in mathematics (Boston, Mass.) ;, v. 92. Contributions Dixmier, Jacques., Connes, Alain. LC Classifications QA387 .O64 1990 Pagination xvi, 579 p. ; Number of Pages 579 Open Library OL1888357M ISBN 10 0817634894, 3764334894 LC Control Number 90049716

Abstract. This chapter deals with *-representations of enveloping algebras. Though some of the considerations and of the main results (e.g., Theorem ) are valid for general *-representations, we aim to present a detailed study of integrable representations.   It is well known today that the theory of vertex operator algebra unifies representation theory of many infinite dimensional Lie algebras via locality. So it is natural to have a notion of unitary vertex operator algebra so that in the case of Virasoro and affine Kac–Moody algebras, these two unitarities are equivalent.   Abstract. In this chapter we collect background material on quantized universal enveloping algebras. We give in particular a detailed account of the construction of the braid group action and PBW-bases, and discuss the finite dimensional representation theory in the setting that the base field $$\mathbb {K}$$ is an arbitrary field and the deformation parameter \(q \in \mathbb . C ∗-algebras (pronounced "C-star") are subjects of research in functional analysis, a branch of mathematics.A C*-algebra is a Banach algebra together with an involution satisfying the properties of the adjoint.A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties. A is a topologically closed set in the norm.