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Models of the symmetric Fock algebra. (English. Russian original) Zbl 1013.81503
Math. Notes 60, No. 6, 710-713 (1996); translation from Mat. Zametki 60, No. 6, 939-942 (1996).
Let $$\Lambda$$ be a $$\mathbb{Z}_2$$-graded superalgebra. For $$H$$ a separable Hilbert space, the $$\Lambda$$-superspace over $$H$$ is defined to be the $$\mathbb{Z}_2$$-graded $$\Lambda$$-module $$H_\Lambda= \Lambda\otimes H$$. Two models of the Fock $$\Lambda$$-superspace and their properties are studied in terms of a so-called supermeasure on $$H_\Lambda$$.

MSC:
 81S05 Commutation relations and statistics as related to quantum mechanics (general) 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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References:
 [1] J. Kupsch,Rev. Math. Phys.,2, No. 4, 457–477 (1990). · Zbl 0722.46039 [2] Y. Haba and J. Kupsch,Forschr. Phys.,45, No. 1, 41–66 (1995). [3] O. G. Smolyanov and E. T. Shavgulidze,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],299, No. 4, 476–482 (1988). [4] O. G. Smolyanov and E. T. Shavgulidze,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],309, No. 3, 545–550 (1989). [5] H. H. Shaefer,Topological Vector Spaces, The Macmillan Co., New York, Collier-Macmillan Limited, London (1966). [6] V. S. Vladimirov and I. V. Volovich,Dokl. Akad. Nauk SSSR [Soviet Math. Dokal.],285, No. 2, 1042–1044 (1985).
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