Quantized Enveloping Algebras Associated with Simple Lie Superalgebras and Their Universal $R$-matrices | Zendy

Hiroyuki Yamane | Zendy

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Quantized Enveloping Algebras Associated with Simple Lie Superalgebras and Their Universal $R$-matrices

Author(s) -

Hiroyuki Yamane

Publication year - 1994

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195166275

Subject(s) - mathematics , simple (philosophy) , pure mathematics , lie superalgebra , lie algebra , universal enveloping algebra , simple lie group , casimir element , killing form , algebra over a field , adjoint representation of a lie algebra , lie conformal algebra , affine lie algebra , current algebra , philosophy , epistemology

O.L In this paper, we introduce a new family of quasi-triangular Hopf algebras coming from complex simple Lie superalgebras. We shall do this by constructing explicitly the associated universal ^-matrices. An outline of our results has been reported in [21]. Let H be a (topological) Hopf algebra. Let & = ̂ at (X) b{ e H (X) H be i an invertible element. Following Drinfeld [4], we say that (J/,A,^) is a quasi-triangular Hopf algebra if it satisfies the following properties:

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