caa a22 4500 606160590 CHVBK 20210128100630.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10468-014-9492-9 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9492-9 PBW Deformations of Skew Group Algebras in Positive Characteristic [Elektronische Daten] [Anne Shepler, Sarah Witherspoon] We investigate deformations of a skew group algebra that arise from a finite group acting on a polynomial ring. When the characteristic of the underlying field divides the order of the group, a new type of deformation emerges that does not occur in characteristic zero. This analogue of Lusztig's graded affine Hecke algebra for positive characteristic can not be forged from the template of symplectic reflection and related algebras as originally crafted by Drinfeld. By contrast, we show that in characteristic zero, for arbitrary finite groups, a Lusztig-type deformation is always isomorphic to a Drinfeld-type deformation. We fit all these deformations into a general theory, connecting Poincaré-Birkhoff-Witt deformations and Hochschild cohomology when working over fields of arbitrary characteristic. We make this connection by way of a double complex adapted from Guccione, Guccione, and Valqui, formed from the Koszul resolution of a polynomial ring and the bar resolution of a group algebra. Springer Science+Business Media Dordrecht, 2014 Graded affine Hecke algebra nationallicence Drinfeld Hecke algebra nationallicence Deformations nationallicence Modular representations nationallicence Hochschild cohomology nationallicence Shepler Anne Department of Mathematics, University of North Texas, 76203, Denton, TX, USA aut Witherspoon Sarah Department of Mathematics, Texas A & M University, 77843, College Station, TX, USA aut Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 257-280 1386-923X 18:1<257 2015 18 10468 https://doi.org/10.1007/s10468-014-9492-9 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/s10468-014-9492-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shepler Anne Department of Mathematics, University of North Texas, 76203, Denton, TX, USA aut NATIONALLICENCE 700 1- Witherspoon Sarah Department of Mathematics, Texas A & M University, 77843, College Station, TX, USA aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 257-280 1386-923X 18:1<257 2015 18 10468