caa a22 4500 606161090 CHVBK 20210128100633.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10468-015-9525-z doi (NATIONALLICENCE)springer-10.1007/s10468-015-9525-z Twisted Semigroup Algebras [Elektronische Daten] [L. Rigal, P. Zadunaisky] We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field K ${\mathbb K}$ . If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec K [ S ] $\mathsf {Spec}~{\mathbb K}[S]$ is an affine toric variety over K ${\mathbb K}$ , and we refer to the twists of K [ S ] ${\mathbb K}[S]$ as quantum affine toric varieties. We show that every quantum affine toric variety has a "dense quantum torus”, in the sense that it has a localization isomorphic to a quantum torus. We study quantum affine toric varieties and show that many geometric regularity properties of the original toric variety survive the deformation process. Springer Science+Business Media Dordrecht, 2015 Noncommutative geometry nationallicence Quantum toric varieties nationallicence Semigroup algebras nationallicence Artin-Schelter nationallicence Cohen-Macaulay nationallicence Artin-Schelter Gorenstein nationallicence Rigal L. Université Paris 13, Sorbonne Paris Cité, LAGA, UMR CNRS 7539, 99 avenue J.-B. Clément, 93430, Villetaneuse, France aut Zadunaisky P. Universidad de Buenos Aires, FCEN, Departamento de Matemáticas, Ciudad Universitaria, Pabellón I, (C1428EGA), Buenos Aires, Argentina aut Algebras and Representation Theory Springer Netherlands 18/5(2015-10-01), 1155-1186 1386-923X 18:5<1155 2015 18 10468 https://doi.org/10.1007/s10468-015-9525-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9525-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rigal L. Université Paris 13, Sorbonne Paris Cité, LAGA, UMR CNRS 7539, 99 avenue J.-B. Clément, 93430, Villetaneuse, France aut NATIONALLICENCE 700 1- Zadunaisky P. Universidad de Buenos Aires, FCEN, Departamento de Matemáticas, Ciudad Universitaria, Pabellón I, (C1428EGA), Buenos Aires, Argentina aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/5(2015-10-01), 1155-1186 1386-923X 18:5<1155 2015 18 10468