Results 31 to 40 of about 3,460 (267)

Extensions of algebraic groups [PDF]

, 2006
Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic group extensions of $G$ by $A$ in terms of a short exact sequence relating the ext-group to a relative second Lie ...
Kumar, S., Neeb, K. -H.
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The classification of extensions of 𝐶*-algebras [PDF]

Bulletin of the American Mathematical Society, 1981
where K = K(H) denotes the compact operators on a separable infinite-dimensional Hubert space H. The addition operation comes from associating to (1.1) its "Busby invariant" [4, Theorem 4.3] A —• Q(B)9 where (1(B) denotes the outer multiplier algebra of B ® K, and then using an injection of (1(B) ® (1(B) into (1(B).
Rosenberg, Jonathan, Schochet, Claude
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Projective varieties have countably many real forms

Comptes Rendus. Mathématique, 2023
In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with a field that has only countably many finite extensions up to isomorphism.
Labinet, Timothée L.
doaj   +1 more source

On the Extensions of Zassenhaus Lemma and Goursat’s Lemma to Algebraic Structures

Journal of Mathematics, 2022
The Jordan–Hölder theorem is proved by using Zassenhaus lemma which is a generalization of the Second Isomorphism Theorem for groups. Goursat’s lemma is a generalization of Zassenhaus lemma, it is an algebraic theorem for characterizing subgroups of the ...
Fanning Meng, Junhui Guo
doaj   +1 more source

Reduced and irreducible simple algebraic extensions of commutative rings [PDF]

Mathematica Moravica, 2017
Let A be a commutative ring with identity and be an algebraic element over A. We give necessary and sufficient conditions under which the simple algebraic extension A[α] is without nilpotent or without idempotent elements.
Mihovski S.V.
doaj  

Algebraic extension of normed algebras [PDF]

Proceedings of the American Mathematical Society, 1956
in B. The classical method of field extension (forming the polynomial ring A [x] and reducing modulo the principal ideal J of 1.1) solves this problem. In this paper, we investigate the role of this process in topological rings. We study the problem of obtaining a normed linear algebra extension B containing a solution of 1.1, where A is a given normed
Arens, Richard, Hoffman, Kenneth
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A Q‐Learning Algorithm to Solve the Two‐Player Zero‐Sum Game Problem for Nonlinear Systems

International Journal of Adaptive Control and Signal Processing, Volume 39, Issue 3, Page 566-581, March 2025.
A Q‐learning algorithm to solve the two‐player zero‐sum game problem for nonlinear systems. ABSTRACT This paper deals with the two‐player zero‐sum game problem, which is a bounded L2$$ {L}_2 $$‐gain robust control problem. Finding an analytical solution to the complex Hamilton‐Jacobi‐Issacs (HJI) equation is a challenging task.
Afreen Islam, Anthony Siming Chen, Guido Herrmann   +2 more
wiley   +1 more source

Discrete Cartesian Coordinate Transformations: Using Algebraic Extension Methods

Applied Sciences
It is shown that it is reasonable to use Galois fields, including those obtained by algebraic extensions, to describe the position of a point in a discrete Cartesian coordinate system in many cases. This approach is applicable to any problem in which the
Aruzhan Kadyrzhan, Dinara Matrassulova, Yelizaveta Vitulyova, Ibragim Suleimenov   +3 more
doaj   +1 more source

Extensions of hereditary algebras

Manuscripta Mathematica, 1984
Let k be an algebraically closed field, B the path algebra over k of an oriented Dynkin diagram of type \(E_ 6,E_ 7\), or \(E_ 8\), and M an indecomposable right B-module. The author determines the representation type (finite, tame or wild) of the matrix algebra \(\left( \begin{matrix} k\\ 0\end{matrix} \begin{matrix} M\\ B\end{matrix} \right)\) for ...
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Adaptive Observer for Coupled Wave PDE and Infinite ODE With Sampled Data and Unknown Input: Application to Brain Hemodynamics Estimation

International Journal of Adaptive Control and Signal Processing, EarlyView.
This article proposes a convergent adaptive observer for a damped wave PDE and an infinite‐dimensional ODE coupled in cascade using sampled‐in‐space ODE state measurements. The proposed observer estimates the distributed states of the PDE and ODE along with unknown PDE parameters and spatial input.
Zehor Belkhatir, Sarah Mechhoud, Taous‐Meriem Laleg‐Kirati   +2 more
wiley   +1 more source