Structure of a finite non-commutative algebra set by a sparse multiplication table

Non-commutative combinatorial algebra

SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A FUZZY SET

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

STORING A SPARSE TABLE bY

The problem of storing and searching large sparse tables arises in compiling and in other areas of computer science. The standard technique for storing such tables is hashing, but hashing has poor worst-case performance. We consider good worst-case methods for storing a table of n entries, each an integer between 0 and N-l . For dynamic tables, in which look-ups and table additions are intermix...

Non Commutative Finite Dimensional Manifolds Ii: Moduli Space and Structure of Non Commutative 3-spheres

This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge between noncommutative differential geometry and its purely algebraic counterpart. It allows to construct a morphism from an involutive quadratic algebras to a C*-...

A non-commutative Minkowskian spacetime from a quantum AdS algebra

A quantum deformation of the conformal algebra of the Minkowskian spacetime in (3 + 1) dimensions is identified with a deformation of the (4 + 1)-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known κ-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian sp...