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Electronic Research Announcements
ISSN 1079-6762

On $\mathbf{3}$-graded Lie algebras, Jordan pairs and the canonical kernel function


Author: M. P. de Oliveira
Translated by:
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 142-151
MSC (2000): Primary 32M15; Secondary 22E46, 46E22
Published electronically: December 17, 2003
MathSciNet review: 2029475
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Abstract: We present several embedding results for $3$-graded Lie algebras and KKT algebras that are generated by two homogeneous elements of degrees $1$ and $-1$. 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 $3$-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: http://dx.doi.org/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
Published electronically: December 17, 2003
Additional Notes: The author has been partially supported by FAPESP
Communicated by: Efim Zelmanov