We show that the spectrum of the locally convex nonstandard hull of an infinite dimensional Grassmann algebra contains a nontrivial analytic part.

Let F be a field of characteristic zero and let E the Grassmann algebra an infinite dimensional F-vector space L. In this paper we study superalgebra structures (that is Z2-gradings) that admits. By using duality between superalgebras automorphisms order at most 2 prove in many cases Z2-graded polynomial identities for such coincide with “typical” E?, Ek? Ek where vector L homogeneous. Recall t...

In this work we provide a new short proof of Carlitz’s identity for the Bernoulli numbers. Our approach is based on the ordinary generating function for the Bernoulli numbers and a Grassmann-Berezin integral representation of the Bernoulli numbers in the context of the Zeon algebra, which comprises an associative and commutative algebra with nilpotent generators.

This paper presents a formalization of Grassmann-Cayley algebra [6] that has been done in the Coq [2] proof assistant. The formalization is based on a data structure that represents elements of the algebra as complete binary trees. This allows to define the algebra products recursively. Using this formalization, published proofs of Pappus’ and Desargues’ theorem [7,1] are interactively derived....

An expression in the exterior algebra of a Peano space yielding Pappus' theorem was originally given by Doubilet, Rota, and Stein [Doubilet, P., Rota, G.-C. & Stein, J. (1974) Stud. Appl. Math. 8, 185-216]. Motivated by an identity of Rota, I give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the theorem of Pappus.

This report is based on review paper [1]. Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the Z p+1 Potts model on a chain. Finite dimensional paragrassmann representations for GL q (2) are constructed. Generalizations of grassmann al...

h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.