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Standard basis in supersymplectic algebras. (English) Zbl 0699.15013

The authors use combinatorial methods for investigating supersymplectic algebras. A standard basis for products of Pfaffians is found in Theorem 4. Applications on the theory of invariants are obtained; in Theorems 5 and 6 the authors have found the form of weak supersymmetric invariants of the Pfaffian algebra of degree n. In addition, an extension of Weyl’s well-known theorem of the syzygies of the Pfaffian is obtained.
Reviewer: P.Koshlukov

MSC:

15A72 Vector and tensor algebra, theory of invariants
17B45 Lie algebras of linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields
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