We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the constants are not “closed” in suitable senses. We also improve the definitions and results from [15] on generalized strongly normal extensions, using this to...

A differential central simple algebra, and in particular a differential matrix algebra, over a differential field K with constants C can be trivialized by a Picard–Vessiot (differential Galois) extension E. In the matrix algebra case, there is a correspondence between K algebras trivialized by E and representations of the Galois group of E over K in PGLn(C), which can be interpreted as cocyles ...

In this work, linearized multivariate skew polynomials over division rings are introduced. Such right linear the corresponding centralizer and generalize polynomial finite fields, group or differential rings. Their natural evaluation is connected to remainder-based of free polynomials. It shown that P-independent sets those given by linearly independent when partitioned into conjugacy classes. ...

In this paper we verify Navarro's refinement of the McKay conjecture for quasi-simple groups Lie type in their defining characteristic. takes into account action specific Galois automorphisms on characters presents [12] . Our proof case relies a character correspondence constructed by Maslowski [11] Building inductive condition from [14] most

Coding, transmission and recovery of quantum states with high security and efficiency, and with as low fluctuations as possible, is the main goal of quantum information protocols and their proper technical implementations. The paper deals with this promise focusing on the quantum states related to Galois algebras. We first review the constructions of complete sets of mutually unbiased bases in ...

Let E/F be a finite and Galois extension of non-archimedean local fields. G connected reductive group defined over E let M:=RE/FG the F obtained by Weil restriction scalars. We investigate depth, enhanced Langlands correspondence, in transition from G(E) to M(F). obtain depth-comparison formula for Weil-restricted groups.

Abstract The Alexandrov L -fuzzy nearness is a new addition to the systems that base for intelligent and its wide applications in various fields. This paper represents connections among such as: rough sets, semi-topogenous orders uniformities complete residuated lattices. Moreover, we show there Galois correspondence between categories of those mentioned systems.