publication . Preprint . 2000

On Associative Conformal Algebras of Linear Growth

Retakh, Alexander;
Open Access English
  • Published: 25 May 2000
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We introduce the notions of conformal identity and unital associative conformal algebras and classify finitely generated simple unital associative conformal algebras of linear growth. These are precisely the complete algebras of conformal endomorphisms of finite modules.
arXiv: Quantitative Biology::Biomolecules
free text keywords: Mathematics - Quantum Algebra, Mathematics - Rings and Algebras, 16P90, 17B69
Download from

[Bl] R.Block, Determination of the differentiably simple rings with a minimal ideal, Ann. of Math. 90 (1969), 433-459.

[Bo] R.Borcherds, Vertex Algebras, Kac-Moody algebras, and the Monster, Proc. Natl. Acad. Sci. USA 83 (1986), 3068-3071.

[DK] A.D'Andrea, V.Kac, Structure theory of finite conformal algebras, Selecta Math. 4 (1998), 377-418.

[H] I.Herstein, Noncommutative Rings, Carus Mathematical Monographs, 15, MAA, 1968.

[K1] V.Kac, Vertex Algebra for Beginners, 2nd ed.(1 ed., 1996), AMS, 1998.

[K2] V.Kac, Formal distribution algebras and conformal algebras, XIIth International Congress of Mathematical Physics (ICMP'97) (Brisbane), Int. Press, 1999, pp. 80-97.

[KL] G.Krause, T.Lenagan, Growth of Algebras and Gelfand-Kirillov Dimension, Pitman Adv. Publ. Program, 1985.

[Li] H.-S.Li, Local systems of vertex operators, vertex superalgebras and modules, J.Pure Appl. Algebra 109 (1996), 143-195.

[Po] E.Posner, Differentiably simle rings, Proc. Amer. Math. Soc. 11 (1960), 337-343. [OpenAIRE]

[R] L.Rowen, Ring Theory, Academic Press, 1989.

[Ro] M.Roitman, On free conformal and vertex algebras, J. Algebra 217 (1999), no. 2, 496-527.

[SSW] L.Small, J.T.Stafford, R.Warfield, Affine algebras of Gelfand-Kirillov dimension one are PI, Math. Proc. Cambridge Phil. Soc. 97 (1985), no. 3, 407-414.

[SW] L.Small, R.Warfield, Prime affine algebras of Gel'fand-Kirillov dimension one, J. Algebra 91 (1984), no. 2, 386-389. [OpenAIRE]

D.Wright, On the Jacobian conjecture, Illinois J. Math 25, no. 3, 423-440.

Department of Mathematics, Yale University, New Haven, CT, 06520 E-mail address:

Any information missing or wrong?Report an Issue