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On  -graded Lie algebras, Jordan pairs and the canonical kernel function
Author(s):
M.
P.
de Oliveira
Journal:
Electron. Res. Announc. Amer. Math. Soc.
9
(2003),
142-151.
MSC (2000):
Primary 32M15;
Secondary 22E46, 46E22
Posted:
December 17, 2003
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Abstract:
We present several embedding results for  -graded Lie algebras and KKT algebras that are generated by two homogeneous elements of degrees  and  . We also propose the canonical kernel function for a ``universal Bergman kernel'' which extends the usual Bergman kernel on a bounded symmetric domain to a group-valued function or, in terms of formal series, to an element in the formal completion of the universal enveloping algebra of the free  -graded Lie algebra in a pair of generators.
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Additional Information:
M.
P.
de Oliveira
Affiliation:
Department of Mathematics, University of Toronto, Canada
Email:
mpdeoliv@math.toronto.edu
DOI:
10.1090/S1079-6762-03-00122-7
PII:
S 1079-6762(03)00122-7
Keywords:
Bergman kernel,
symmetric domain,
$3$-graded Lie algebra
Received by editor(s):
October 11, 2001,
Received by editor(s) in revised form:
October 6, 2003
Posted:
December 17, 2003
Additional Notes:
The author has been partially supported by FAPESP
Communicated by:
Efim Zelmanov
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