Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 


Restricted cohomology of modular Witt algebras

Authors: Tyler J. Evans, Alice Fialowski and Michael Penkava
Journal: Proc. Amer. Math. Soc. 144 (2016), 1877-1886
MSC (2010): Primary 17B50, 17B56; Secondary 17B68, 17B66
Published electronically: November 30, 2015
MathSciNet review: 3460150
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we compute the restricted 0, $ 1$-, and $ 2$-dimensional cohomology groups with trivial coefficients of the modular Witt algebras $ W$ for any prime $ p>3$, and give explicit description of all one-dimensional restricted central extensions of $ W$.

References [Enhancements On Off] (What's this?)

  • [1] Richard E. Block, On the Mills-Seligman axioms for Lie algebras of classical type, Trans. Amer. Math. Soc. 121 (1966), 378-392. MR 0188356 (32 #5795)
  • [2] D. B. Fuks and Tyler J. Evans, On the structure of the restricted Lie algebra for the Witt algebra in a finite characteristic, Funktsional. Anal. i Prilozhen. 36 (2002), no. 2, 69-74, 96 (Russian, with Russian summary); English transl., Funct. Anal. Appl. 36 (2002), no. 2, 140-144. MR 1922020 (2003f:17020),
  • [3] Tyler J. Evans and Dmitry Fuchs, A complex for the cohomology of restricted Lie algebras, J. Fixed Point Theory Appl. 3 (2008), no. 1, 159-179. MR 2402915 (2009e:17035),
  • [4] D. B. Fuks, Cohomology of infinite-dimensional Lie algebras, Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986. Translated from the Russian by A. B. Sosinskiĭ. MR 874337 (88b:17001)
  • [5] D. B. Fuchs and I. M. Gelfand, Cohomology of the Lie algebra of vector fields on a circle, Functional Analysis and Its Applications, 2:342-343, 1968.
  • [6] J. E. Humphreys, Existence of Levi factors in certain algebraic groups, Pacific J. Math. 23 (1967), 543-546. MR 0218365 (36 #1452)
  • [7] J. E. Humphreys, Restricted Lie algebras (and beyond), Algebraists' homage: papers in ring theory and related topics (New Haven, Conn., 1981) Contemp. Math., vol. 13, Amer. Math. Soc., Providence, R.I., 1982, pp. 91-98. MR 685939 (84d:17012)
  • [8] Nathan Jacobson, Abstract derivation and Lie algebras, Trans. Amer. Math. Soc. 42 (1937), no. 2, 206-224. MR 1501922,
  • [9] N. Jacobson, Restricted Lie algebras of characteristic $ p$, Trans. Amer. Math. Soc. 50 (1941), 15-25. MR 0005118 (3,103g)
  • [10] Jens Carsten Jantzen, Representations of algebraic groups, 2nd ed., Mathematical Surveys and Monographs, vol. 107, American Mathematical Society, Providence, RI, 2003. MR 2015057 (2004h:20061)
  • [11] George J. McNinch, Levi decompositions of a linear algebraic group, Transform. Groups 15 (2010), no. 4, 937-964. MR 2753264 (2012b:20110),
  • [12] M. Schottenloher, A mathematical introduction to conformal field theory, 2nd ed., Lecture Notes in Physics, vol. 759, Springer-Verlag, Berlin, 2008. MR 2492295 (2011a:81219)
  • [13] F. V. Weinstein, Filtering bases: a tool to compute cohomologies of abstract subalgebras of the Witt algebra, Unconventional Lie algebras, Adv. Soviet Math., vol. 17, Amer. Math. Soc., Providence, RI, 1993, pp. 155-216. MR 1254731 (94k:17042)
  • [14] N. N. Yakovlev, Cohomologies of Witt algebras, Functional Analysis and Its Applications, 9(3):269-271, July-September 1975.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17B50, 17B56, 17B68, 17B66

Retrieve articles in all journals with MSC (2010): 17B50, 17B56, 17B68, 17B66

Additional Information

Tyler J. Evans
Affiliation: Department of Mathematics, Humboldt State University, Arcata, California 95521

Alice Fialowski
Affiliation: Institute of Mathematics, Eötvös Loránd University, H-1117 Budapest Hungary

Michael Penkava
Affiliation: Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, Wisconsin 54701

Received by editor(s): February 16, 2015
Received by editor(s) in revised form: May 18, 2015
Published electronically: November 30, 2015
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society