Graded Morita theory over a G-graded G-acted algebra

The G-graded Identities of the Grassmann Algebra

Let G be a finite abelian group with identity element 1G and L = ⊕ g∈G L g be an infinite dimensional G-homogeneous vector space over a field of characteristic 0. Let E = E(L) be the Grassmann algebra generated by L. It follows that E is a G-graded algebra. Let |G| be odd, then we prove that in order to describe any ideal of G-graded identities of E it is sufficient to deal with G′-grading, whe...

Ordinary I?o(g)-graded Cohomology

Let G be a compact Lie group. What is the appropriate generalization of singular cohomology to the category of G-spaces XI The simplest choice is the ordinary cohomology of EG xG X, where EG is the total space of a universal principal G-bundle. This Borel cohomology [1] is readily computable and has many applications, but is clearly inadequate for such basic parts of G-homotopy theory as obstru...

Differential Graded Algebra

Differential Graded Algebra

g-BDI: A Graded Intensional Agent Model for Practical Reasoning

In intentional agents, actions are derived from the mental attitudes and their relationships. In particular, preferences (positive desires) and restrictions (negative desires) are important proactive attitudes which guide agents to intentions and eventually to actions. In this paper we overview recent developments about a multi-context based agent architecture g-BDI to represent and reasoning a...