Invariant traces on algebras
HTML articles powered by AMS MathViewer
- by Guido Karrer
- Proc. Amer. Math. Soc. 42 (1974), 369-372
- DOI: https://doi.org/10.1090/S0002-9939-1974-0327838-8
- PDF | Request permission
Abstract:
Certain properties of traces on a finite-dimensional associative algebra A lead to the definition of an element $t(A) \in {H^1}({\text {Out}}\;A,{C^\ast }),{C^\ast }$ being the multiplicative group of the center of A as Out A-module. It is shown that $t(A) = 0$ is equivalent to the existence of nondegenerate traces on A which are invariant under composition with all automorphisms of A. In particular, by means of Galois theory, $t(A) = 0$ is shown for a semisimple algebra A, whereas $t(A) \ne 0$ for certain group algebras.References
- Bruno Harris, Commutators in division rings, Proc. Amer. Math. Soc. 9 (1958), 628–630. MR 96697, DOI 10.1090/S0002-9939-1958-0096697-4
- Akira Hattori, Rank element of a projective module, Nagoya Math. J. 25 (1965), 113–120. MR 175950 S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
- B. L. van der Waerden, Algebra. Teil I, Heidelberger Taschenbücher, Band 12, Springer-Verlag, Berlin-New York, 1966 (German). Siebte Auflage. MR 0263581
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 369-372
- MSC: Primary 16A64
- DOI: https://doi.org/10.1090/S0002-9939-1974-0327838-8
- MathSciNet review: 0327838