The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
V. V. Bavula - One of the best experts on this subject based on the ideXlab platform.
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The classical left regular left quotient ring of a ring and its Semisimplicity criteria
Journal of Algebra and Its Applications, 2017Co-Authors: V. V. BavulaAbstract:Let [Formula: see text] be a ring, [Formula: see text] and [Formula: see text] be the set of regular and left regular elements of [Formula: see text] ([Formula: see text]). Goldie’s Theorem is a Semisimplicity criterion for the classical left quotient ring [Formula: see text]. Semisimplicity criteria are given for the classical left regular left quotient ring [Formula: see text]. As a corollary, two new Semisimplicity criteria for [Formula: see text] are obtained (in the spirit of Goldie).
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The classical left regular left quotient ring of a ring and its Semisimplicity criteria
Journal of Algebra and Its Applications, 2017Co-Authors: V. V. BavulaAbstract:Let R be a ring, 𝒞R and ′𝒞 R be the set of regular and left regular elements of R (𝒞R⊆′𝒞 R). Goldie’s Theorem is a Semisimplicity criterion for the classical left quotient ring Ql,cl(R) := 𝒞R−1R. Semisimplicity criteria are given for the classical left regular left quotient ring ′Q l,cl(R) :=′𝒞 R−1R. As a corollary, two new Semisimplicity criteria for Ql,cl(R) are obtained (in the spirit of Goldie).
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The classical left regular left quotient ring of a ring and its Semisimplicity criteria
arXiv: Rings and Algebras, 2015Co-Authors: V. V. BavulaAbstract:Let $R$ be a ring, $\CC_R$ and $\pCCR$ be the set of regular and left regular elements of $R$ ($\CC_R\subseteq \pCCR$). Goldie's Theorem is a Semisimplicity criterion for the classical left quotient ring $Q_{l,cl}(R):=\CC_R^{-1}R$. Semisimplicity criteria are given for the classical left regular left quotient ring $'Q_{l,cl}(R):=\pCCR^{-1}R$. As a corollary, two new Semisimplicity criteria for $Q_{l,cl}(R)$ are obtained (in the spirit of Goldie).
Charles John Read - One of the best experts on this subject based on the ideXlab platform.
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Semisimplicity of B(E)
Journal of Functional Analysis, 2005Co-Authors: Matthew Daws, Charles John ReadAbstract:We study the semi-simplicity of the second dual of the Banach algebra of operators on a Banach space, B(E)″, endowed with either Arens product. It was previously shown that if E is a Hilbert space, then B(E) is Arens regular and B(E)″ is semi-simple. We show that for a large class of Banach spaces E, including subspaces of Lp spaces not isomorphic to a Hilbert space, B(E)″ is not semi-simple. This is achieved by deriving a new representation of B(lp)′, and then constructing a member of the radical of B(lp)″, for p≠2.
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Semisimplicity of B(E) 00
2004Co-Authors: Matthew Daws, Charles John ReadAbstract:We study the semi-simplicity of the second dual of the Banach algebra of operators on a Banach space, B(E) 00 , endowed with either Arens product. It was previously shown that if E is a Hilbert space, then B(E) is Arens regular and B(E) 00 is semisimple. We show that for a large class of Banach spaces E, including subspaces of L p spaces not isomorphic to a Hilbert space, B(E) 00 is not semi-simple. This is achieved by deriving a new representation of B(l p ) 0 , and then constructing a member of the radical of B(l p ) 00 , for p 6 2.
Bavula V.v. - One of the best experts on this subject based on the ideXlab platform.
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The classical left regular left quotient ring of a ring and its Semisimplicity criteria
'World Scientific Pub Co Pte Lt', 2016Co-Authors: Bavula V.v.Abstract:Let R be a ring, CR and ′ CR be the set of regular and left regular elements of R (CR ⊆ ′ CR). Goldie’s Theorem is a Semisimplicity criterion for the classical left quotient ring Ql,cl(R) := C −1 R R. Semisimplicity criteria are given for the classical left regular left quotient ring ′Ql,cl(R) := ′ C −1 R R. As a corollary, two new Semisimplicity criteria for Ql,cl(R) are obtained (in the spirit of Goldie)
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The classical left regular left quotient ring of a ring and its Semisimplicity criteria
2015Co-Authors: Bavula V.v.Abstract:Let $R$ be a ring, $\CC_R$ and $\pCCR$ be the set of regular and left regular elements of $R$ ($\CC_R\subseteq \pCCR$). Goldie's Theorem is a Semisimplicity criterion for the classical left quotient ring $Q_{l,cl}(R):=\CC_R^{-1}R$. Semisimplicity criteria are given for the classical left regular left quotient ring $'Q_{l,cl}(R):=\pCCR^{-1}R$. As a corollary, two new Semisimplicity criteria for $Q_{l,cl}(R)$ are obtained (in the spirit of Goldie).Comment: 22 page
Daniel Tubbenhauer - One of the best experts on this subject based on the ideXlab platform.
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Semisimplicity of hecke and walled brauer algebras
Journal of The Australian Mathematical Society, 2017Co-Authors: Henning Haahr Andersen, Catharina Stroppel, Daniel TubbenhauerAbstract:We show how to use Jantzen’s sum formula for Weyl modules to prove Semisimplicity criteria for endomorphism algebras of $\mathbf{U}_{q}$ -tilting modules (for any field $\mathbb{K}$ and any parameter $q\in \mathbb{K}-\{0,-1\}$ ). As an application, we recover the Semisimplicity criteria for the Hecke algebras of types $\mathbf{A}$ and $\mathbf{B}$ , the walled Brauer algebras and the Brauer algebras from our more general approach.
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Semisimplicity of Hecke and (walled) Brauer algebras
Journal of the Australian Mathematical Society, 2016Co-Authors: Henning Haahr Andersen, Catharina Stroppel, Daniel TubbenhauerAbstract:We show how to use Jantzen's sum formula for Weyl modules to prove Semisimplicity criteria for endomorphism algebras of $\textbf{U}_q$-tilting modules (for any field $\mathbb{K}$ and any parameter $q\in\mathbb{K}-\{0,-1\}$). As an application, we recover the Semisimplicity criteria for the Hecke algebras of types $\textbf{A}$ and $\textbf{B}$, the walled Brauer algebras and the Brauer algebras from our more general approach.
Akio Tamagawa - One of the best experts on this subject based on the ideXlab platform.
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Geometric monodromy -- Semisimplicity and maximality
Annals of Mathematics, 2017Co-Authors: Anna Cadoret, Chun Yin Hui, Akio TamagawaAbstract:Let X be a connected scheme, smooth and separated over an alge- braically closed field k of characteristic p ≥ 0, let f: Y → X be a smooth proper morphism and x a geometric point on X. We prove that the tensor invariants of bounded length ≤ d of π1(X; x) acting on the etale cohomology groups H*(Yx; Fl) are the reduction modulo-l of those of π1(X, x) acting on H*(Yx, ℤl) for l greater than a constant depending only on f: Y → X, d. We apply this result to show that the geometric variant with Fl-coefficients of the Grothendieck-Serre Semisimplicity conjecture - namely, that π1(X, x) acts semisimply on H*(Yx, Fl) for l ≫ 0-is equivalent to the condition that the image of π1(X, x) acting on H*(Yx;Ql) is 'almost maximal' (in a precise sense; what we call 'almost hyperspecial') with respect to the group of Ql-points of its Zariski closure. Ultimately, we prove the geometric variant with Fl-coefficients of the Grothendieck-Serre Semisimplicity conjecture.
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Geometric monodromy -- Semisimplicity and maximality
arXiv: Number Theory, 2017Co-Authors: Anna Cadoret, Chun Yin Hui, Akio TamagawaAbstract:Let $X$ be a connected scheme, smooth and separated over an algebraically closed field $k$ of characteristic $p\geq 0$, let $f:Y\rightarrow X$ be a smooth proper morphism and $x$ a geometric point on $X$. We prove that the tensor invariants of bounded length $\leq d$ of $\pi_1(X,x)$ acting on the etale cohomology groups $H^*(Y_x,F_\ell)$ are the reduction modulo-$\ell$ of those of $\pi_1(X,x)$ acting on $H^*(Y_x,Z_\ell)$ for $\ell$ greater than a constant depending only on $f:Y\rightarrow X$, $d$. We apply this result to show that the geometric variant with $F_\ell$-coefficients of the Grothendieck-Serre Semisimplicity conjecture -- namely that $\pi_1(X,x)$ acts semisimply on $H^*(Y_x,F_\ell)$ for $\ell\gg 0$ -- is equivalent to the condition that the image of $\pi_1(X,x)$ acting on $H^*(Y_x,Q_\ell)$ is `almost maximal' (in a precise sense; what we call `almost hyperspecial') with respect to the group of $Q_\ell$-points of its Zariski closure. Ultimately, we prove the geometric variant with $F_\ell$-coefficients of the Grothendieck-Serre Semisimplicity conjecture.
