Abstract
The only noncommutative ring for which the real spectrum has been described so far is the quantum affine ring R q [x,y] [J. Algebra 212 (1999) 190]. The aim of this paper is to describe the real spectra of quantum affine rings k q [x 1 ,…,x n ] where k is a formally real affine R -algebra and q ∈M n ( R + ) . As a by-product we describe the real spectra of quantized enveloping algebra U q ( s l 2 ( R )) and quantum special linear group O q (SL 2 ( R )) . Formal reality and semireality is characterized for the following classes of quantum groups: quantum affine rings, quantized enveloping algebras, quantized function algebras, quantized Weyl algebras.
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