Linear Algebra and Group Theory for Physicists pp 179-230 | Cite as

# Representations of Linear Associative Algebras

Chapter

## Abstract

We recall from section (2.5) that a linear associative algebra or a hyper complex system is a linear vector space which is closed with respect to an associative multiplication and that it may also be regarded as a ring with an external domain of scalar operators. We also introduced in section (4.3) the concept of the Regular Representation, the carrier space for which was the algebra itself regarded as a vector space. In its role as a ring, it is also the represented object in the sense that each element of the algebras is mapped into matrix of the representation.

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## References

- 1.
**E. Artin, C.J. Nesbitt**and**R.M. Thrall**,*Rings with minimum condition*, Ann Arbor, University of Michigan Press, 1944.zbMATHGoogle Scholar - 2.
**H. Boerner**,*Representations of groups; with special consideration for the needs of modern physics*, [2d rev. ed.], Amsterdam, North-Holland Pub. Co., 1970.zbMATHGoogle Scholar - 3.
**N. Jacobson**,*Lectures in Abstract Algebra Vols. 1 and 2*, New-York, Springer-Verlag, 1975, (c1951–1964).Google Scholar - 4.
**B.L. Van der Waerden**,*Modern algebra*vols I,II, (In part a development from lectures by E. Art in and E. Noether) New York, F. Ungar, c1950–c1953Google Scholar - 5.
**H. Weyl***The classical groups; their invariants and representations*, by Hermann Weyl … Princeton, N.J., Princeton University Press; London, Oxford University Press, 1939.zbMATHGoogle Scholar - 6.
**H. Weyl***The theory of groups and quantum mechanics*. Translated from the 2d rev. German ed. by H.P. Robertson, New York, Dover Publications, 1950.zbMATHGoogle Scholar

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