On enveloping skew fields of some lie superalgebras
Jacques Alev (LM-Reims), Fran\c{c}ois Dumas
TL;DR
This paper investigates the structure of skew fields of fractions associated with enveloping algebras of certain Lie superalgebras, comparing them to classical Weyl skew fields to understand their algebraic properties.
Contribution
It explicitly determines the skew fields of fractions for osp(1, 2) and some subalgebras of osp(1, 4), highlighting differences from classical cases.
Findings
Skew fields of osp(1, 2) are characterized.
Comparison with Weyl skew fields reveals new structural insights.
Results extend understanding of superalgebra enveloping algebra fractions.
Abstract
We determine the skew fields of fractions of the enveloping algebra of the Lie superalgebra osp(1, 2) and of some significant subsu-peralgebras of the Lie superalgebra osp(1, 4). We compare the kinds of skew fields arising from this "super" context with the Weyl skew fields in the classical Gelfand-Kirillov property.
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