Abstract. There are several research elds called noncommutative algebraic geome-try. In this note, we will introduce the one founded by M. Artin. Roughly speaking,

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation

Duality is one of the fundamental concepts in mathematics. The most basic duality is that of linear algebra. We take a vector space V over a field K and assign to it V ∗ = HomK(V,K). If V is finite dimensional then V ∼ = V ∗∗. This can be generalized in many ways. For instance we can make V

In this lecture I would like to address the following question: given an associative algebra A0, what are the possible ways to deform it? Consideration of this question for concrete algebras often leads to interesting mathematical discoveries. I will discuss several approaches to this question

. In this dissertation, algorithms for noncommutative algebra, when ab is not necessarily equal to ba, are examined with practical implementations in mind. Different encodings of associative algebras and modules are also considered. To effectively analyze these algorithms and encodings, the encoding neutral analysis

Throughout this paper H is a finite-dimensional Hopf algebra over a field k, andA is a associative k-algebra. Unless it is stated additionally, all tensor products are over k. Definition 1.1 It is said that H acts on A, if A is left H-module and for any h ∈ H, a, b ∈ A

Abstract not found

Abstract not found

Abstract not found

To Mamuka Jibladze on occasion of his 50th birthday Abstract. We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which