Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30174
1−Skeleton Resolution of Free Simplicial Algebras with Given CW−Basis

Authors: Ali Mutlu, Berrin Mutlu

Abstract:

In this paper we use the definition of CW basis of a free simplicial algebra. Using the free simplicial algebra, it is shown to construct free or totally free 2−crossed modules on suitable construction data with given a CW−basis of the free simplicial algebra. We give applications free crossed squares, free squared complexes and free 2−crossed complexes by using of 1(one) skeleton resolution of a step by step construction of the free simplicial algebra with a given CW−basis.

Keywords: Free crossed square, Free 2−crossed modules, Free simplicial algebra, Free square complexes, Free 2−crossed complexes CW−basis, 1−skeleton. A. M. S.Classification:[2000] 18D35, 18G30, 18G50, 18G55, 55Q05, 55Q20.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062574

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 758

References:


[1] Z. ARVASI and T. PORTER . Freeness conditions for 2-Crossed modules of Commutative Algebras. Applied Categorical Structure 181 (1998), 426-448.
[2] R. BROWN. Coproduct of crossed P-modules, application to second homotopy groups and to the homology of groups. Topology 23 (1984), 337-345.
[3] G.J. ELLIS. Crossed squares and combinatorial homotopy. Math. Z. 214 (1993), 93-110.
[4] A.R. GRANDJE 'AN and M.J. VALE . 2-Modulos Cruzados en la Cohomologia de Andr'e-Quillen. Memorias de la Real Academia de Ciencias. 22 (1986).
[5] A. MUTLU . Free 2−crossed complexes of simplicial algebras. Mathematical and Computational Applications 5(1) (2000), 13-22.
[6] A.MUTLU, B. MUTLU AND E. USLU To construction of free simplicial algebras with given CW-basis. International Mathematical Forum, 4 (30) (2009), 1489 - 1495.
[7] A. MUTLU AND T. PORTER , Freeness conditions for 2−crossed modules and complexes. Theory and Applications Categories 4 (8) (1998), 174-194.
[8] N.M. SHAMMU. Algebraic and Categorical Structure of Category of Crossed Modules of Algebras Ph.D. Thesis, University of Wales, Bangor (1992).