In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over finitely presented Koszul Auslander-regular algebra has trivial homological determinant. For A = ?(R)<x1, x2> connected R, compute its P-determinant and inverse ?. particular case quasi-commutative extensions Artin-Schelter regular algebras, show explicitly connection between ring coefficients exten...

New developments on non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a scalar field is coupled to a Chern Simons gauge field, a geometrical phase emerges for vortex like solutions, transformed by Galilei boosts. hep-th/0411139 Non commutative solito...

The mutual relation between quantum Micro and classical Macro is clarified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested. 1 Sectors as Quantum-Classical Boundary To fix the setting of my discussion, let me start from ...

Cline-Parshall-Scott introduced the concept of quasi-hereditary algebras (§2.5) to study highest weight categories in the representation theory of Lie algebras and algebraic groups [CPS1,2]. Quasi-hereditary algebras were effectively applied in the representation theory of artin algebras as well by Dlab-Ringel [DR1,2,3] and many other authors. On the other hand, in the representation theory of ...

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

Cline-Parshall-Scott introduced the concept of quasi-hereditary algebras (§2.5) to study highest weight categories in the representation theory of Lie algebras and algebraic groups [CPS1,2]. Quasi-hereditary algebras were effectively applied in the representation theory of artin algebras as well by Dlab-Ringel [DR1,2,3] and many other authors. On the other hand, in the representation theory of ...