# IJPAM: Volume 53, No. 4 (2009)

**UNIVERSAL CENTRAL EXTENSIONS OF COMPLEX SIMPLE**

LIE ALGEBRAS EXTENDED OVER

LIE ALGEBRAS EXTENDED OVER

Department of Mathematics for Economic and Social Sciences

University of Bologna

5, Viale Filopanti, Bologna, 40126, ITALY

e-mail: [email protected]

**Abstract.**In this paper, a vector bundle
over
with fiber
is constructed, where
is the algebra of regular functions on
the linear algebraic group
, and denotes a Borel subgroup
of
. As well, an imbedding of
into
,
the algebra of holomorphic sections of the previous bundle, is explicitly given. Moreover,
an inclusion of the universal central extension
of the Lie
algebra
, with a simple complex finite dimensional Lie algebra, into the universal central extension of the Lie algebra
is proved.

**Received: **May 13, 2009

**AMS Subject Classification: **14F05, 17B65

**Key Words and Phrases: **vector bundle, universal central extension, algebraic group

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 53

**Issue:** 4