| 单词 | exterior algebra |
| 释义 | > as lemmasexterior algebra exterior algebra n. Mathematics and Physics (a) an algebra (algebra n. 2b) consisting of the quotient algebra T(V)/I (where T(V) is the tensor algebra of a vector space V and, for every x in V, I is the two-sided ideal generated by all elements of the form x ⊗ x), and in which the exterior product is taken as the product operation; (also) any of several analogous algebras based on structures other than vector spaces; (b) the branch of algebra concerned with the study and applications of exterior algebras and exterior products.The exterior algebra of a vector space V is typically denoted by Λ(V).Exterior algebras are useful in physics in the study of fermions and supersymmetry, and more generally in the area of differential geometry. ΚΠ 1951 Trans. Amer. Math. Soc. 70 244 It seems that the questions of mixed volumes are best handled with the techniques of tensor spaces and the exterior algebra. 1963 W. H. Greub Linear Algebra ix. 133 (title) Duality in exterior algebra. 1991 R. L. Bryant et al. Exterior Differential Syst. viii. 320 One of the most useful facts in exterior algebra is the familiar Cartan Lemma. 2013 G. Grensing Struct. Aspects Quantum Field Theory I. xxiv. 606 The exterior algebra of a vector space offers a natural approach to the concept of differential forms. < as lemmas |
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