scholarly journals Multiparameter quantum function algebra at roots of 1

1996 ◽  
Vol 306 (1) ◽  
pp. 759-780 ◽  
Author(s):  
M. Costantini ◽  
M. Varagnolo
Keyword(s):  
Function Algebra ◽  
Quantum Function

On the Quantum Function Algebra at Roots of One

2004 ◽  
Vol 32 (6) ◽  
pp. 2377-2383 ◽  
Author(s):  
Mauro Costantini
Keyword(s):  
Function Algebra ◽  
Quantum Function

scholarly journals PBW THEOREMS AND FROBENIUS STRUCTURES FOR QUANTUM MATRICES

2007 ◽  
Vol 49 (3) ◽  
pp. 479-488
Author(s):  
FABIO GAVARINI
Keyword(s):  
Function Algebra ◽  
Direct Application ◽  
Hopf Subalgebra ◽  
Frobenius Morphism ◽  
Quantum Matrices ◽  
Root Of Unity ◽  
Frobenius Structures ◽  
Quantum Function

AbstractLet $G \in \{{\it Mat}_n(\C), {GL}_n(\C), {SL}_n(\C)\}$, let $\Oqg$ be the quantum function algebra – over $\Z [q,q^{-1}]$ – associated to G, and let $\Oeg$ be the specialisation of the latter at a root of unity ϵ, whose order ℓ is odd. There is a quantum Frobenius morphism that embeds $\Og,$ the function algebra of G, in $\Oeg$ as a central Hopf subalgebra, so that $\Oeg$ is a module over $\Og$. When $G = {SL}_n(\C)$, it is known by [3], [4] that (the complexification of) such a module is free, with rank ℓdim(G). In this note we prove a PBW-like theorem for $\Oqg$, and we show that – when G is Matn or GLn – it yields explicit bases of $\Oeg $ over $ \Og$ over $\Og,$. As a direct application, we prove that $\Oegl$ and $\Oem$ are free Frobenius extensions over $\Ogl$ and $\Om$, thus extending some results of [5].

scholarly journals Quantum Function Algebra at Roots of 1

1994 ◽  
Vol 108 (2) ◽  
pp. 205-262 ◽  
Author(s):  
C. Deconcini ◽  
V. Lyubashenko
Keyword(s):  
Function Algebra ◽  
Quantum Function

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

Boundaries for a Real Function Algebra

2020 ◽  
pp. 136-163
Author(s):  
S. H. Kulkarni ◽  
B.V. Limaye
Keyword(s):  
Real Function ◽  
Function Algebra ◽  
Real Function Algebra

Gleason Parts of a Real Function Algebra

2020 ◽  
pp. 89-135
Author(s):  
S. H. Kulkarni ◽  
B.V. Limaye
Keyword(s):  
Real Function ◽  
Function Algebra ◽  
Real Function Algebra
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