Electronic Research Announcements

On $\mathbf{3}$ -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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