Minimal varieties of PI-superalgebras with graded involution

Polynomial identities of some minimal varieties with low PI - exponent

-graded Poincaré superalgebras

Using colored superanalysis and ε-Lie superalgebras, we build the minimal Poincaré superalgebra in the case of the Z n grading. We then build a representation of this algebra, and the corresponding Poincaré supergroup.

Graded Lie Superalgebras, Supertrace Formula, and Orbit Lie Superalgebras

Let Γ be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a (Γ × A)-graded Lie superalgebra L = ⊕ (α,a)∈Γ×A L(α,a) by Lie superalgebra automorphisms preserving the (Γ × A)-gradation. In this paper, we show that the Euler-Poincaré principle yields the generalized denominator identity for L and derive a clos...

Structures Preserved by Consistently Graded Lie Superalgebras

I construct systems of generalized Pfaff equations (of the form α = 0, α some differential forms), preserved by the exceptional Lie superalgebras ksle(5|10), vle(3|6) and mb(3|8). This yields an intrinsic geometric definition of these algebras. The analogous construction for the contact superalgebra k(1|m) (a.k.a. the centerless N = m superconformal algebra) is reviewed.

On Involution Rings with Unique Minimal *-subring

The structure of certain involution rings having a unique minimal *-subring, is described.