We study the projective linear group PGL2(A) associated with an arbitrary algebra A, and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles Möbius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the Möbius group μev(M) defined by Connes and st...

We study the projective linear group PGL 2 (A) associated with an arbitrary algebra A and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles M obius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the Mobius group ev (M) de ned by Connes and...

In this paper, an incremental learning algorithm based on extraction of action sequence is proposed. The proposed method extracts action sequences from experience obtained through learning in previously encountered environments and uses them in current environments . The proposed method is constructed by two modules. The first module is an action module that uses neural network and genetic algo...

We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on the affine plane.

In this paper we present a collaborative artificial intelligence (AI) module for a turn-based, multiplayer, environmental awareness game. The game is a version of the EnerCities serious game, modified in the context of a European-Union project to support sequential plays of an emphatic robotic tutor interacting with two human players in a social and pedagogical manner. For that purpose, we crea...

An original digital signature scheme based on action of infinite ring on module is presented. It is assumed that the ring contains an infinite multiplicative monoid. The ring action is defined as monoid elements's action on the module element as an operator. The signature scheme is based on particularly designed one–way functions (OWFs), using a postulated hard problem in monoid action level. T...

The action of the symmetric group Sn on the set Parkn of parking functions of size n has received a great deal of attention in algebraic combinatorics. We prove that the action of Sn on Parkn extends to an action of Sn+1. More precisely, we construct a graded Sn+1-module Vn such that the restriction of Vn to Sn is isomorphic to Parkn. We describe the Sn-Frobenius characters of the module Vn in ...

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...