Polyhedral realizations of crystal bases B(λ) for quantum algebras of nonexceptional affine types

2019 ◽  
Vol 60 (9) ◽  
pp. 091704
Author(s):  
A. Hoshino ◽  
K. Nakada
Keyword(s):  
Quantum Algebras ◽  
Crystal Bases

scholarly journals Polyhedral realizations of crystal bases for quantum algebras of finite types

2005 ◽  
Vol 46 (11) ◽  
pp. 113514 ◽  
Author(s):  
Ayumu Hoshino
Keyword(s):  
Quantum Algebras ◽  
Crystal Bases

Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Rank 2

2006 ◽  
Vol 34 (6) ◽  
pp. 1997-2018 ◽  
Author(s):  
Ayumu Hoshino
Keyword(s):  
Quantum Algebras ◽  
Crystal Bases ◽  
Rank 2

scholarly journals Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Type A

2005 ◽  
Vol 33 (7) ◽  
pp. 2167-2191 ◽  
Author(s):  
Ayumu Hoshino ◽  
Toshiki Nakashima
Keyword(s):  
Type A ◽  
Quantum Algebras ◽  
Crystal Bases

Polyhedral realizations of crystal bases for quantum algebras of classical affine types

2013 ◽  
Vol 54 (5) ◽  
pp. 053511 ◽  
Author(s):  
A. Hoshino
Keyword(s):  
Quantum Algebras ◽  
Crystal Bases

scholarly journals Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

Canonical Bases of Modified Quantum Algebras for TypeA2-monomial Elements

2015 ◽  
Vol 43 (9) ◽  
pp. 3663-3685 ◽  
Author(s):  
Weideng Cui
Keyword(s):  
Quantum Algebras ◽  
Canonical Bases

scholarly journals Crystal Bases and Monomials forUq(G2)-Modules

2006 ◽  
Vol 34 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Dong-Uy Shin
Keyword(s):  
Crystal Bases

Discrete series of unitary irreducible representations of the U q (u(3, 1)) and U q (u(n, 1)) noncompact quantum algebras

2011 ◽  
Vol 74 (6) ◽  
pp. 808-823
Author(s):  
Yu. F. Smirnov ◽  
R. M. Asherova
Keyword(s):  
Discrete Series ◽  
Irreducible Representations ◽  
Quantum Algebras

scholarly journals Degenerate Sklyanin algebras

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Andrey Smirnov
Keyword(s):  
Difference Operators ◽  
Baxter Equation ◽  
Quantum Algebras ◽  
Rational Solutions ◽  
R Matrix ◽  
Gauge Transformations ◽  
Sklyanin Algebras ◽  
Sklyanin Algebra ◽  
The Difference

AbstractNew trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

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