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Polynomial identity rings as rings of functions | | Zinovy Reichstein
; Nikolaus Vonessen
; | | Date: |
9 Jul 2004 | | Subject: | Rings and Algebras; Algebraic Geometry MSC-class: 16R30, 16R20 (Primary) 14L30, 14A10 (Secondary) | math.RA math.AG | | Abstract: | We generalize the usual relationship between irreducible Zariski closed subsets of the affine space, their defining ideals, coordinate rings, and function fields, to a non-commutative setting, where "varieties" carry a PGL_n-action, regular and rational "functions" on them are matrix-valued, "coordinate rings" are prime polynomial identity algebras, and "function fields" are central simple algebras of degree n. In particular, a prime polynomial identity algebra of degree n is finitely generated if and only if it arises as the "coordinate ring" of a "variety" in this setting. For n = 1 our definitions and results reduce to those of classical affine algebraic geometry. | | Source: | arXiv, math.RA/0407152 | | Services: | Forum | Review | PDF | Favorites | |
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