S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Journal Papers (저널논문_수리과학부)
Graded Lie superalgebras and the superdimension formula
- Seok-Jin, Kang
- Issue Date
- J. Algebra 204 (1998), 597-655
- In this paper, we investigate the structure of graded Lie superalgebras = (, a) × (, a), where is a countable abelian semigroup and is a countable abelian group with a coloring map satisfying a certain finiteness condition. Given a denominator identity for the graded Lie superalgebra , we derive a superdimension formula for the homogeneous subspaces (, a) ( , a ), which enables us to study the structure of graded Lie superalgebras in a unified way. We discuss the applications of our superdimension formula to free Lie superalgebras, generalized Kac–Moody superalgebras, and Monstrous Lie superalgebras. In particular, the product identities for normalized formal power series are interpreted as the denominator identities for free Lie superalgebras. We also give a characterization of replicable functions in terms of product identities and determine the root multiplicities of Monstrous Lie superalgebras.
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