An application of representation theory to PI-algebras
HTML articles powered by AMS MathViewer
- by Jørn B. Olsson and Amitai Regev PDF
- Proc. Amer. Math. Soc. 55 (1976), 253-257 Request permission
Abstract:
By realizing that the multilinear identities of degree $n$ of a $PI$-algebra form a left ideal in the group algebra $F[{S_n}]$, it is possible sometimes to use the representation theory of the symmetric group ${S_n}$ in the study of $T$-ideals and $PI$-algebras. In this note we demonstrate this method by proving: Theorem. If the codimensions of a $PI$-algebra are bounded, then they are eventually bounded by $1$.References
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
- Adalbert Kerber, Representations of permutation groups. I, Lecture Notes in Mathematics, Vol. 240, Springer-Verlag, Berlin-New York, 1971. MR 0325752
- A. A. Klein and A. Regev, The codimensions of a $\textrm {PI}$-algebra, Israel J. Math. 12 (1972), 421–426. MR 325673, DOI 10.1007/BF02764633
- D. Krakowski and A. Regev, The polynomial identities of the Grassmann algebra, Trans. Amer. Math. Soc. 181 (1973), 429–438. MR 325658, DOI 10.1090/S0002-9947-1973-0325658-5
- Dudley E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups, Oxford University Press, New York, 1940. MR 0002127
- Amitai Regev, Existence of identities in $A\otimes B$, Israel J. Math. 11 (1972), 131–152. MR 314893, DOI 10.1007/BF02762615 *. W. Burnside, Theorem of groups of finite order, 2nd ed., Cambridge, 1911.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 253-257
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399154-1
- MathSciNet review: 0399154