We describe the construction of non-commutative manifolds, which are the non-commutative analogs of homogeneous spaces using coherent states. In the commutative limit we obtain standard manifolds. Applications to the Fuzzy sphere and to the Fuzzy hyperboloid are discussed in more detail. *) Part of Project Nr. P8916-PHY of the \Fonds zur FF orderung der wissenschaftlichen Forschung in Osterreich".

Let Γ be a finite graph and GΓ be the corresponding free partially commutative group. In this paper we construct orthogonality theory for graphs and free partially commutative groups. The theory developed here provides tools for the study of the structure of the centraliser lattice of partially commutative groups.

Robert Lee Wilson Department of Mathematics Rutgers University The determinant of a matrix with entries in a commutative ring is a main organizing tool in commutative algebra. In these lectures, we present an analogous theory, the theory of quasideterminants, for matrices with entries in a not necessarily commutative ring. The theory of quasideterminants was originated by I. Gelfand and V. Retakh.

This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and associative-commutative unification problems are W [1]-hard. A fixed-parameter algorithm and a polynomialtime algorithm are presented for special cases of commutat...

Parikh’s Theorem says that the commutative image of every context free language is the commutative image of some regular set. Pilling has shown that this theorem is essentially a statement about least solutions of polynomial inequalities. We prove the following general theorem of commutative Kleene algebra, of which Parikh’s and Pilling’s theorems are special cases: Every finite system of polyn...

1. DERIVED GEOMETRY WITH L∞ ALGEBRAS We are interested in studying formal derived moduli problems, as an orienting remark recall that particularly nice simplicial sets are those that are Kan complexes and that the nerve of a category C is Kan complex if and only if C is a groupoid. Consider the following progression. • Schemes: Functors from commutative algebras to sets; • Stacks: Functors from...

This paper is an expanded version of [28] and [30] where there is presented an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical observation naturally occurs in a context of non-commutative algebra. In this way a formalism similar to quantum mechanics occurs first, but not necessarily with the usual ...

In this letter we propose a possible mechanism of leftand right-handed neutrino couplings to photons, which arises quite naturally in non-commutative gauge field theory. We estimate the predicted additional energy-loss in stars induced by space-time non-commutativity. The usual requirement that any new energy-loss mechanism in globular stellar clusters should not excessively exceed the standard...

In this paper we prove that a finite partial commutative (idempotent commutative) Latin square can be embedded in a finite commutative (idempotent commutative) Latin square. These results are then used to show that the loop varieties defined by any non-empty subset of the identities {x(xy) = y, (yx)x = y} and the quasi-group varieties defined by any non-empty subset of {x” = x, x(xy) = y, (yx)x...

In [Ans08a, Ans08b], we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of examples, demonstrating what these general results look like for the most important states on non-commutative polynomials, namely for various product states. In particular,...