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Tensor spaces and exterior algebra. Translated from the Japanese by T. Yokonuma. (English) Zbl 0754.15028
Translations of Mathematical Monographs. 108. Providence, RI: American Mathematical Society (AMS). x, 131 p. (1992).
Summary: This book provides an introduction to tensors and related topics. The book begins with definitions of the basic concepts of the theory; tensor products of vector spaces, tensors, tensor algebras and exterior algebra. Their properties are then studied and applications given. Algebraic systems with bilinear multiplications are introduced in the final chapter. In particular, the theory of replicas of Chevalley and several properties of Lie algebras that follow from this theory are presented.

MSC:
15A69Multilinear algebra, tensor products
15A75Exterior algebra, Grassmann algebras
15-01Textbooks (linear algebra)
17BxxLie algebras; Lie superalgebras