Translation principle in the category O for the Virasoro algebra.

Format:

Book

Thesis/Dissertation

Author/Creator:

Movshev, Michael V.

Contributor:

Larsen, Michael, advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Mathematics.

0405.

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

0405.

Physical Description:

40 pages

Contained In:

Dissertation Abstracts International 58-03B.

System Details:

Mode of access: World Wide Web.

text file

Summary:

Representations of the Virasoro algebra are the main ingredient of Conformal Field Theory. This explains a very close attention to it from physicists and mathematicians. The Virasoro algebra has many features in common with finite dimensional semi-simple Lie algebras. In particular the category O has a splitting into the direct sum of "elementary" subcategories $O\sb\theta.$ A classical result in representation theory of semi-simple Lie algebras asserts that there is a finite set of equivalence classes of subcategories $O\sb\theta.$ This is why one is led to conjecture this property for the Virasoro algebra. Very detailed knowledge of projective objects in O is the main technical moment in our approach to this problem. The main result is that this conjecture does not hold. We exhibit an invariant which distinguishes some categories which are to be equivalent due to the conjecture. We hope that our results will help to understand the real nature of the Riemann correspondence for the Virasoro algebra.

Notes:

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 1997.

Source: Dissertation Abstracts International, Volume: 58-03, Section: B, page: 1323.

Adviser: Michael Larsen.

Local Notes:

School code: 0175.

ISBN:

9780591363722

Access Restriction:

Restricted for use by site license.