Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-30T08:12:57.186Z Has data issue: false hasContentIssue false
  • English
  • Français

Generic Lie colour algebras

Published online by Cambridge University Press:  17 April 2009

Kenneth L. Price
Kenneth L. Price
Affiliation:
Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI 54901-8631, United States of America e-mail: pricek@uwosh.edu
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe a type of Lie colour algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Gröbner basis methods can be used to study universal enveloping algebras of factors of generic Lie colour algebras.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 327 - 335
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Aubry, M. and Lemaire, J.-M., ‘Zero divisors in enveloping algebras of graded Lie algebras’, J. Pure Appl. Algebra 38 (1985), 159–166.CrossRefGoogle Scholar
[2]Bahturin, Yu. A., Mikhalev, A.A., Petrogradsky, V.M. and Zaicev, M.V., Infinite dimensional Lie superalgebras (DeGruyter, Berlin, 1992).CrossRefGoogle Scholar
[3]Behr, E.J., ‘Enveloping algebras of Lie superalgebras’, Pacific J. Math. 130 (1987), 9–25.CrossRefGoogle Scholar
[4]Bell, A.D., ‘A criterion for primeness of enveloping algebras of Lie superalgebras’, J. Pure Appl. Algebra 69 (1990), 111–120.CrossRefGoogle Scholar
[5]Bøgvad, R., ‘Some elementary results on the cohomology of graded Lie algebras’, in Homotopie Algébrique et Algèbre Locale (Luminy, 1982), Astérisque 113–114 (Soc. Math. France, Paris, 1984), pp. 156–166.Google Scholar
[6]Bueso, J.L., Castro-Jiménez, F.J., Gómez-Torrecillas, J. and Lobillo, F. J., ‘Homological computations in PBW modules’, Algebr. Represent. Theory 4 (2001), 201–218.CrossRefGoogle Scholar
[7]Bueso, J.L., Castro-Jiménez, F.J., Gómez-Torrecillas, J. and Lobillo, F. J., ‘An introduction to effective calculus in quantum groups’, in Rings, Hopf algebras and Brauer Groups, (Caenepell, S. and Verschoren, A., Editors), Lecture Notes in Pure and Applied Mathematics 197 (Marcel Dekker, New York, 1998), pp. 55–83.Google Scholar
[8]Bueso, J.L., Castro-Jiménez, F.J., Gómez-Torrecillas, J. and Lobillo, F.J., ‘Primality test in iterated ore extensions’, Comm. Algebra 29 (2001), 1357–1371.CrossRefGoogle Scholar
[9]Kirkman, E., Kuzmanovich, J. and Small, L., ‘Finitistic dimensions of Noetherian rings’, J. Algebra 147 (1992), 350–364.CrossRefGoogle Scholar
[10]Le Bruyn, L., ‘Trace rings of generic 2 by 2 matrices’, Mem. Amer. Math. Soc. 66 (1987).Google Scholar
[11]McConnell, J.C. and Robson, J.C., Noncommutative Noetherian rings (Wiley, Chichester, England, 1987).Google Scholar
[12]Price, K.L., ‘Homological properties of color Lie super algebras’, in Advances in Ring Theory (Granville, OH, 1996), (Jain, S.K. and Rizvi, S. Tariq, Editors) (Birkhäuser, 1997), pp. 287–293.CrossRefGoogle Scholar
[13]Price, K.L., ‘Primeness criterion for universal enveloping algebras of Lie color algebras’, J. Algebra 235 (2001), 589–607.CrossRefGoogle Scholar