Results 21 to 30 of about 8,728,657 (238)
Bimodule structure of central simple algebras
Journal of Algebra, 2017 For a maximal separable subfield $K$ of a central simple algebra $A$, we provide a semiring isomorphism between $K$-$K$-bimodules $A$ and $H$-$H$ bisets of $G = \Gal(L/F)$, where $F = \operatorname{Z}(A)$, $L$ is the Galois closure of $K/F$, and $H = \Gal(L/K)$. This leads to a combinatorial interpretation of the growth of $\dim_K((KaK)^i)$, for fixed $
Eliyahu Matzri +3 more
openaire +3 more sources
Almost nilpotent Lie algebras [PDF]
, 1987 Throughout we shall consider only finite-dimensional Lie algebras over a field of characteristic zero. In [3] it was shown that the classes of solvable and of supersolvable Lie algebras of dimension greater than two are characterised by the structure of ...
Towers, David
core +4 more sources
Cohomological invariants of odd degree Jordan algebras [PDF]
, 2008 In this paper we determine all possible cohomological invariants of Aut(J)-torsors in Galois cohomology with mod 2 coefficients (characteristic of the base field not 2), for J a split central simple Jordan algebra of odd degree n ≥ 3.
MacDonald, Mark
core +4 more sources
Differential Central Simple Algebras
, 2023 Differential central simple algebras are the main object of study in this survey article. We recall some crucial notions such as differential subfields, differential splitting fields, tensor products etc. Our main focus is on differential splitting fields which connects these objects to the classical differential Galois theory. We mention several known
Gupta, Parul +2 more
openaire +2 more sources
Invariants de Witt des involutions de bas degré en caractéristique 2
Comptes Rendus. MathématiqueA $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated to every symplectic involution on a central simple algebra of degree $8$ over a field of characteristic $2$.
Tignol, Jean-Pierre
doaj +1 more source
Generators of Central Simple Algebras
Journal of Algebra, 1998 Let \(A\) be a central simple algebra with centre \(K\). Given a subfield \(k\) of \(K\) and \(z_1,\dots,z_m\in A\), the subalgebra \(k(z_1,\dots,z_m)\) of \(A\) is defined by taking the \(k\)-algebra \(B\) generated by \(z_1,\dots,z_m\) and localizing at all elements of \(B\cap K^\times\).
openaire +2 more sources
Essential dimension of central simple algebras
Acta Mathematica, 2012 Let \(F\) be a base field, and let \(\mathcal F\colon Fields/F\to Sets\) be a functor from the category of field extensions of \(F\) to the category of sets. An element \(\alpha\in\mathcal F(E)\) is said to be defined over a subfield \(K\) of \(E\) if \(\alpha\) is in the image of the morphism \(\mathcal F(K)\to\mathcal F(E)\). The essential dimension \
Baek, S Baek, Sanghoon +1 more
openaire +4 more sources
Advanced Functional Materials, EarlyView.An organic neuromorphic architecture for the classification of human motor behavior is presented and validated. It performs somatic integration by linearly combining the activity from three muscles. An investigation of synaptic weights is presented and discussed in relationship with the classification performance.
Ilenia Sergi +7 more
wiley +1 more source
Organic Materials of Tomorrow: Horizons of Artificial Intelligence
Advanced Materials, EarlyView.This review examines machine learning techniques accelerating the discovery of organic semiconductors by linking molecular structure to properties. Key methods include graph neural networks, generative models, and active learning. Applications to organic photovoltaics demonstrate practical impact.
Harold Mena +3 more
wiley +1 more source