Abstract
We express the double affine Hecke algebra ℍ associated to the general linear group GL2(k) (here, k is a field with char(k) ≠ 2) as an amalgamated free product of quadratic extensions over the three-dimensional quantum torus 𝒪q((k×)3). With an eye towards proving ring-theoretic results pertaining to ℍ, a general treatment of amalgamated products of Ore and quadratic extensions is given. We prove an analogue of the Hilbert Basis Theorem for an amalgamated product Q of quadratic extensions and determine conditions for when the one-sided ideals of Q are principal or doubly-generated. Furthermore, we determine sufficient conditions which imply Q is a principal ideal ring. Finally, we construct an explicit isomorphism from ℍ to the amalgamated free product ring of quadratic extensions over 𝒪q((k×)3), a ring known to be noetherian. Therefore, it follows that ℍ is noetherian.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
