Categorical structures of Lie–Rinehart crossed module

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

In this paper we give constructions of pullback, finite product, finite limit, coproduct, colimit, pushout, etc.in a special full subcategory XMod/L of the category of Lie–Rinehart crossed modules.

PDF

___

[1] Borceux F. Handbook of Categorical Algebra 1. New York, NY, USA: Cambridge, 1994.
[2] Casas JM. Obstructions to Lie-Rinehart algebra extensions. Algebr Colloq 2011; 18: 83-104.
[3] Casas JM, Ladra M, Pirashvili T. Crossed modules for Lie-Rinehart algebras. J Algebra 2004; 274: 192-201.
[4] Casas JM, Ladra M, Pirashvili T. Triple cohomology of Lie-Rinehart algebras and the canonical class of associative algebras. J Algebra 2005; 291: 144-163.
[5] Herz J. Pseudo-algèbres de Lie. Cr Acad Sci 1953; 236: 1935-1937 (in French).
[6] Huebschmann J. Poisson cohomology and auantization. J Reine Angew Math 1990; 408: 57-113.
[7] Mackenzie K. Lie Groupoids and Lie Algebroids in Differential Geometry. Cambridge, UK: Cambridge University Press, 1987.
[8] Shammu NM. Algebraic and categorical structure of category of crossed modules of algebras. PhD, University College of North Wales, Bangor, UK, 1992.
[9] Whitehead JHC. Combinatorial homotopy. B Am Math Soc 1949; 55: 453-496.