A Galois-theoretic approach to Kanev’s correspondence

A Galois-theoretic Approach to Kanev’s Correspondence

Let G be a finite group, Λ an absolutely irreducible Z[G]-module and w a weight of Λ. To any Galois covering with group G we associate two correspondences, the Schur and the Kanev correspondence. We work out their relation and compute their invariants. Using this, we give some new examples of Prym-Tyurin varieties.

A Galois-Theoretic Approach to the Covering Theory of Quandles

The purpose of this article is to clarify the relationship between the algebraic notion of quandle covering introduced by M. Eisermann and the categorical notion of covering arising from Galois theory. A crucial role is played by the adjunction between the variety of quandles and its subvariety of trivial quandles.

Introduction to the Galois correspondence

GALOIS: An Order-Theoretic Approach to Conceptual Clustering

The theory of concept (or Galois) lattices provides a natural and formal setting in which to discover and represent concept hierarchies. In this paper we present a system, GALOIS, which is able to determine the concept lattice corresponding to a given set of objects. GALOIS is incremental and relatively efficient, the time complexity of each update ranging from O(n) to O(n2) where n is the numb...

The Galois Correspondence

Example 1.1. Two R-automorphisms of C are the identity z 7→ z and complex conjugation z 7→ z. We will show they are the only ones. If σ : C→ C is an R-automorphism, then for any real a and b we have σ(a+ bi) = σ(a) +σ(b)σ(i) = a+ bσ(i), so σ is determined by σ(i) and i = −1 =⇒ σ(i) = σ(−1) =⇒ σ(i) = −1 =⇒ σ(i) = ±i. If σ(i) = i, then σ(z) = z for all z ∈ C and if σ(i) = −i, then σ(z) = z for al...