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Some exceptional compact matrix pseudogroups. (English) Zbl 0763.17008

For complex Lie algebras of classical type, representations of their quantized enveloping algebras have been used to construct compact matrix pseudogroups, e.g. by M. Rosso [Duke Math. J. 61, 11-40 (1990; Zbl 0721.17013)]. In the paper under review, the author does this for Lie algebras of types \(E_ 6\) and \(E_ 7\). Besides considering finite dimensional representations of complex Hopf algebras, the author also uses real forms of quantized enveloping algebras, which give rise to \(*\)- Hopf algebras.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)

Citations:

Zbl 0721.17013
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References:

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