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A remark on finitely presented infinite-dimensional algebras


Authors: Gilbert Baumslag and Peter B. Shalen
Journal: Proc. Amer. Math. Soc. 108 (1990), 633-635
MSC: Primary 16A45; Secondary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1990-0991690-7
MathSciNet review: 991690
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Abstract: By estimating dimensions of representation varieties, we show that certain finitely presented algebras are infinite dimensional.


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

  • [1] G. Baumslag and P. B. Shalen, Affine algebraic sets and some finitely presented algebras, in Essays in group theory, Mathematical Sciences Research Institute Publications 8, Springer-Verlag, New York, Heidelberg, Berlin 1987, pp. 1-14. MR 919827 (89b:20071)
  • [2] J. E. Humphreys, Linear algebraic groups, Graduate Texts in Mathematics 21, Springer-Verlag, New York, Heidelberg, Berlin, 1981. MR 0396773 (53:633)
  • [3] J. Levitzki, On a problem of A. Kurosh, Bull. Amer. Math. Soc. 52 (1946), 1033-1035. MR 0019600 (8:435a)
  • [4] C. Procesi, Finite dimensional representations of algebras, Israel J. Math. 19 (1974), 169-182. MR 0357507 (50:9975)

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DOI: https://doi.org/10.1090/S0002-9939-1990-0991690-7
Article copyright: © Copyright 1990 American Mathematical Society

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