An Interesting Dual Galois Correspondence

1967 ◽  
Vol 74 (8) ◽  
pp. 991
Author(s):  
W. A. LaBach
Keyword(s):  
Galois Correspondence

The Galois correspondence

Galois Theory ◽  
1989 ◽  
pp. 104-107
Author(s):  
Ian Stewart
Keyword(s):  
Galois Correspondence

scholarly journals Categories of L-Fuzzy Čech Closure Spaces and L-Fuzzy Co-Topological Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1274
Author(s):  
Irina Perfilieva ◽  
Ahmed A. Ramadan ◽  
Enas H. Elkordy
Keyword(s):  
Computer Science ◽  
Fuzzy Systems ◽  
Topological Spaces ◽  
Fuzzy Relations ◽  
Approximation Spaces ◽  
Galois Correspondence ◽  
Closure Spaces

Recently, fuzzy systems have become one of the hottest topics due to their applications in the area of computer science. Therefore, in this article, we are making efforts to add new useful relationships between the selected L-fuzzy (fuzzifying) systems. In particular, we establish relationships between L-fuzzy (fuzzifying) Čech closure spaces, L-fuzzy (fuzzifying) co-topological spaces and L-fuzzy (fuzzifying) approximation spaces based on reflexive L-fuzzy relations. We also show that there is a Galois correspondence between the categories of these spaces.

scholarly journals A Note on the Galois Correspondence for Commutative Rings

1996 ◽  
Vol 183 (1) ◽  
pp. 266-272 ◽  
Author(s):  
A. Carboni ◽  
G. Janelidze ◽  
A.R. Magid
Keyword(s):  
Commutative Rings ◽  
Galois Correspondence

scholarly journals EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS

2011 ◽  
Vol 10 (05) ◽  
pp. 995-1106 ◽  
Author(s):  
MARIE-CLAUDE DAVID ◽  
NICOLAS M. THIÉRY
Keyword(s):  
Automorphism Groups ◽  
Group Algebras ◽  
Self Duality ◽  
Finite Dimensional ◽  
Twisted Group ◽  
Galois Correspondence ◽  
Index 2 ◽  
Original Motivation ◽  
The Way

We study the four infinite families KA(n), KB(n), KD(n), and KQ(n) of finite-dimensional Hopf (in fact Kac) algebras constructed, respectively, by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal sub-algebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we describe.

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