التفاصيل البيبلوغرافية
العنوان: |
Automorphisms of quantum polynomial rings and Drinfeld Hecke algebras. |
المؤلفون: |
Shepler, Anne V., Uhl, Christine |
المصدر: |
Journal of Noncommutative Geometry; 2024, Vol. 18 Issue 3, p803-835, 33p |
مصطلحات موضوعية: |
HECKE algebras, QUANTUM rings, GROUP algebras, AUTOMORPHISMS, COHOMOLOGY theory, HOMOMORPHISMS, QUANTUM groups, POLYNOMIAL rings |
مستخلص: |
We consider quantum (skew) polynomial rings and observe that their graded automorphisms coincide with those of quantum exterior algebras. This allows us to define a quantum determinant that gives a homomorphism of groups acting on quantum polynomial rings. We use quantum subdeterminants to classify the resulting Drinfeld Hecke algebras for the symmetric group, other infinite families of Coxeter and complex reflection groups, and mystic reflection groups (which satisfy a version of the Shephard–Todd–Chevalley theorem). This direct combinatorial approach replaces the technology of Hochschild cohomology used by Naidu and Witherspoon over fields of characteristic zero and allows us to extend some of their results to fields of arbitrary characteristic and also locate new deformations of skew group algebras. [ABSTRACT FROM AUTHOR] |
|
Copyright of Journal of Noncommutative Geometry is the property of European Mathematical Society - EMS - Publishing House GmbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
قاعدة البيانات: |
Complementary Index |