An Excellent Permutation Operator for Cryptographic Applications

2005 ◽  
pp. 317-326 ◽  
Author(s):  
Josef Scharinger
Keyword(s):  
Permutation Operator

Braided GLq(2, C) and its dual space

1994 ◽  
Vol 72 (7-8) ◽  
pp. 336-341
Author(s):  
M. Couture
Keyword(s):  
Hopf Algebras ◽  
Dual Space ◽  
Permutation Operator

We define Hopf algebras that are characterized by Pμ statistics where Pμ is a generalized permutation operator [Formula: see text]. These structures may be viewed as the end result of a deformation of the statistics of GLq(2, C) and Uq(sl(2, C)).

Permutation operator: An explicit representation

1979 ◽  
Vol 47 (2) ◽  
pp. 166-167 ◽  
Author(s):  
G. Bruno Schmid
Keyword(s):  
Explicit Representation ◽  
Permutation Operator

EXTENDED HUBBARD HAMILTONIAN WITH (SUPER)SYMMETRIES: ADDITIVE POLYNOMIAL R-MATRIX FOR SOME INTEGRABLE CASES

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2953-2960 ◽  
Author(s):  
FABRIZIO DOLCINI ◽  
ARIANNA MONTORSI
Keyword(s):  
Spectral Parameter ◽  
One Dimension ◽  
Constructive Method ◽  
Permutation Operator ◽  
R Matrix ◽  
Hubbard Hamiltonian ◽  
Completely Integrable ◽  
Extended Hubbard Hamiltonian ◽  
Second Degree

We propose a constructive method to prove the integrability of a given physical Hamiltonian in one dimension, which amounts to looking for appropriate polynomial R-matrices, solutions of GYBE, whose first coefficient in the power expansion with respect to the spectral parameter is the Hamiltonian itself. The method is applied to the extended Hubbard Hamiltonian, in particular to the cases in which it exhibits so(4) or gl(2,1) symmetries. We show that in the latter case the R-matrices are at most polynomial of second degree, whose coefficients are nothing but the Hamiltonian, the identity and the permutation operator. In this way, all known completely integrable cases are recovered. Also, the method allows to recognize that the possible integrability of the most general gl(2,1) invariant Hamiltonian depends on the existence of a non-additive R-matrix.

Permutation operator: An explicit representation

1981 ◽  
Vol 49 (7) ◽  
pp. 669-671 ◽  
Author(s):  
Dietrich Grau
Keyword(s):  
Explicit Representation ◽  
Permutation Operator
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