2000/05/10 by Phùng Hô Hái, Phung Ho Hai, Hai, Phung Ho
Mathematics · Physics and Astronomy · #16W30 #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:17B37
paper · pdf · doi:10.48550/arxiv.math/0005090
latex 2.09, amsart style, 28 pages
arxiv created 2000/05/10 · openalex publication_date 2000/05/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a Hecke operator R, one defines the matrix bialgebra \ER, which is considered as the function algebra on the quantum space of endomorphisms of the quantum space associated to R. One generalizes this notion, defining the function algebra \MRS on the quantum space of homomorphisms of two quantum spaces associated to two Hecke operators R and S respectively. \MRS can be considered as a quantum analogue (or a deformation) of the function algebra on the variety of matrices of a certain degree. We provide two realiztions of \MRS as a quotient algebra and as a subalgebra of a tensor algebra, whence derive interesting informations about \MRS, for instance the Koszul property, a formula for computing the Poincaré series. On \MRS coact the bialgebras \ER and \ES. We study the two-sided ideals in \MRS, invariant with respect to these actions, in particular, the determinantal ideals. We prove analogies of the fundamental theorems on invariant theory for these quantum groups and quantum hom-spaces.