Links between cofinite prime ideals in quantum function algebras

1997 ◽  
Vol 100 (1) ◽  
pp. 285-308 ◽  
Author(s):  
Ian M. Musson
Keyword(s):  
Prime Ideals ◽  
Function Algebras ◽  
Quantum Function

scholarly journals PRESENTATION BY BOREL SUBALGEBRAS AND CHEVALLEY GENERATORS FOR QUANTUM ENVELOPING ALGEBRAS

2006 ◽  
Vol 49 (2) ◽  
pp. 291-308 ◽  
Author(s):  
Fabio Gavarini
Keyword(s):  
Integral Form ◽  
R Matrix ◽  
Generators And Relations ◽  
Enveloping Algebras ◽  
Function Algebras ◽  
Alternative Approach ◽  
Q Matrix ◽  
Lower Triangular ◽  
Standard Presentation ◽  
Quantum Function

AbstractWe provide an alternative approach to the Faddeev–Reshetikhin–Takhtajan presentation of the quantum group $\uqg$, with $L$-operators as generators and relations ruled by an $R$-matrix. We look at $\uqg$ as being generated by the quantum Borel subalgebras $U_q(\mathfrak{b}_+)$ and $U_q(\mathfrak{b}_-)$, and use the standard presentation of the latter as quantum function algebras. When $\mathfrak{g}=\mathfrak{gl}_n$, these Borel quantum function algebras are generated by the entries of a triangular $q$-matrix. Thus, eventually, $U_q(\mathfrak{gl}_n)$ is generated by the entries of an upper triangular and a lower triangular $q$-matrix, which share the same diagonal. The same elements generate over $\Bbbk[q,q^{-1}]$ the unrestricted $\Bbbk [q,q^{-1}]$-integral form of $U_q(\mathfrak{gl}_n)$ of De Concini and Procesi, which we present explicitly, together with a neat description of the associated quantum Frobenius morphisms at roots of 1. All this holds, mutatis mutandis, for $\mathfrak{g}=\mathfrak{sl}_n$ too.

scholarly journals Degrees of Quantum Function Algebras at Roots of 1

1996 ◽  
Vol 180 (3) ◽  
pp. 897-917 ◽  
Author(s):  
Giovanni Gaiffi
Keyword(s):  
Function Algebras ◽  
Quantum Function

scholarly journals Representations of affine quantum function algebras

2004 ◽  
Vol 272 (2) ◽  
pp. 775-800
Author(s):  
Bharath Narayanan
Keyword(s):  
Function Algebras ◽  
Quantum Function

(α,β)‐derivations on quantum function algebras

1996 ◽  
Vol 37 (5) ◽  
pp. 2527-2552
Author(s):  
L. J. Swank
Keyword(s):  
Function Algebras ◽  
Quantum Function

scholarly journals Quantum function algebras from finite-dimensional Nichols algebras

2020 ◽  
Vol 14 (3) ◽  
pp. 879-911
Author(s):  
Marco Andrés Farinati ◽  
Gastón Andrés García
Keyword(s):  
Finite Dimensional ◽  
Function Algebras ◽  
Nichols Algebras ◽  
Quantum Function

N-ideals of commutative rings

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2933-2941 ◽  
Author(s):  
Unsal Tekir ◽  
Suat Koc ◽  
Kursat Oral
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Proper Ideal ◽  
Prime Ideals ◽  
Nonzero Identity

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

scholarly journals Quantun function algebras as quantum enveloping algebras

1998 ◽  
Vol 26 (6) ◽  
pp. 1795-1818 ◽  
Author(s):  
Fabio Gavarini
Keyword(s):  
Enveloping Algebras ◽  
Function Algebras
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