Lie-algebraic approach to the theory of polynomial solutions. II. Differential equations in one real and one Grassmann variables and 2x2 matrix differential equations ABSTRACT A classification theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solu-tions(the generalized Bochner problem) is given. The main result is based on the consideratio...

We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on C(p+q)·p ∗, the space of (p + q)× p matrices of rank p, invariant under the right action of Gl(p, C) can be regarded as functions on the Grassmann manifold Gp,q(C), but do not form a subalgebra whereas functions only invariant under the unitary subgroup U(p) ⊂ Gl(p,...

We analyse a supersymmetric mechanical model derived from (1+1)-dimensional field theory with Yukawa interaction, assuming that all physical variables take their values in a Grassmann algebra B. Utilizing the symmetries of the model we demonstrate how for a certain class of potentials the equations of motion can be solved completely for any B. In a second approach we suppose that the Grassmann ...

The integral cohomology algebra of $\widetilde G_{6,3}$ has been determined in the recent work Kalafat and Yal\c{c}inkaya. We completely determine G_{n,3}$ for $n=8$ $n=10$. main method used to describe these algebras is Leray-Serre spectral sequence. also illustrate this by determining G_{n,2}$ $n$ odd.

A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over K = R with l 1-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field K with l 1-norm and set of generators of arbitrary power. Any l 1-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain l 1-spa...

The (classical, small quantum, equivariant) cohomology ring of the grassmannianG(k, n) is generated by certain derivations operating on an exterior algebra of a free module of rank n (Schubert Calculus on a Grassmann Algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. It also provides, by results of Laksov and Thor...

Early in the development of computer graphics it was realized that projective geometry is suited quite well to represent points and transformations. Now, maybe another change of paradigm is lying ahead of us based on Geometric Algebra. If you already use quaternions or Lie algebra in additon to the well-known vector algebra, then you may already be familiar with some of the algebraic ideas that...