The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
A. Kawakami - One of the best experts on this subject based on the ideXlab platform.
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A realization method of transfer functions containing variable parameter
Proceedings of IECON'94 - 20th Annual Conference of IEEE Industrial Electronics, 1Co-Authors: A. KawakamiAbstract:Proposes a method for realizing transfer functions containing variable parameters, by the state-space method. By using this method, variable transfer functions (VTF) can be often realized with a Minimal Dimension. For the case that a Minimal realization can not be obtained, the realization Dimension can be reduced. >
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ISCAS - A realization method of the transfer functions containing variable parameter
Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94, 1Co-Authors: A. KawakamiAbstract:In this paper, we propose a method for realizing transfer functions containing a variable parameter, by the state-space method. By using this method, variable transfer functions (VTF) can be often realized with a Minimal Dimension. In case that a Minimal realization can not be obtained, the realization Dimension can be fairly reduced. >
P. Koulmann - One of the best experts on this subject based on the ideXlab platform.
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Minimal Dimension of symmetric or skew-symmetric matrices of given Minimal polynomial
Journal of Pure and Applied Algebra, 2001Co-Authors: P. KoulmannAbstract:Over a field k of characteristic not 2 the set of Minimal polynomials of symmetric or skew-symmetric matrices (with respect to an involution of the first kind) is known. We give the smallest possible Dimension of a symmetric or skew-symmetric matrix of given Minimal polynomial depending on the type of the involution. Concerning the transpose, we give the smallest constant c such that any suitable polynomial f is the Minimal polynomial of a symmetric (resp. skew-symmetric) matrix of Dimension c deg f. The case of polynomials of degree 2 is completely solved. (C) 2001 Elsevier Science B.V. All rights reserved.
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Minimal Dimension of symmetric or skew-symmetric matrices of given Minimal polynomial
Journal of Pure and Applied Algebra, 2001Co-Authors: P. KoulmannAbstract:AbstractOver a field k of characteristic not 2 the set of Minimal polynomials of symmetric or skew-symmetric matrices (with respect to an involution of the first kind) is known. We give the smallest possible Dimension of a symmetric or skew-symmetric matrix of given Minimal polynomial depending on the type of the involution. Concerning the transpose, we give the smallest constant c such that any suitable polynomial f is the Minimal polynomial of a symmetric (resp. skew-symmetric) matrix of Dimension cdegf. The case of polynomials of degree 2 is completely solved
Ian J. Leary - One of the best experts on this subject based on the ideXlab platform.
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An Eilenberg-Ganea Phenomenon for Actions with Virtually Cyclic Stabilisers
arXiv: Group Theory, 2012Co-Authors: Martin Fluch, Ian J. LearyAbstract:In Dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the Minimal Dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological Dimension is 2 while the Bredon geometric Dimension is 3.
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On Algebraic and Geometric Dimensions for Groups with Torsion
Journal of the London Mathematical Society, 2001Co-Authors: Noel Brady, Ian J. Leary, Brita E. A. NucinkisAbstract:We argue that the geometric Dimension of a discrete group G ought to be defined to be the Minimal Dimension of a model for the universal proper G-space rather than the Minimal Dimension of a model for the universal free G-space. For torsion-free groups, these two quantities are equal, but the new quantity can be finite for groups containing torsion whereas the old one cannot. There is an analogue of cohomological Dimension (defined in terms of Bredon cohomology) for which analogues of the Eilenberg-Ganea and Stalling-Swan theorems (due to W. Lueck and M. J. Dunwoody respectively) hold. We show that some groups constructed by M. Bestvina and M. Davis provide counterexamples to the analogue of the Eilenberg-Ganea conjecture.
Nadina Rojas - One of the best experts on this subject based on the ideXlab platform.
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faithful representations of Minimal Dimension of current heisenberg lie algebras
International Journal of Mathematics, 2009Co-Authors: Leandro Cagliero, Nadina RojasAbstract:Given a Lie algebra 𝔤 over a field of characteristic zero k, let μ(𝔤) = min{dim π : π is a faithful representation of 𝔤}. Let 𝔥m be the Heisenberg Lie algebra of Dimension 2m + 1 over k and let k[t] be the polynomial algebra in one variable. Given m ∈ ℕ and p ∈ k[t], let 𝔥m, p = 𝔥m ⊗ k[t]/(p) be the current Lie algebra associated to 𝔥m and k[t]/(p), where (p) is the principal ideal in k[t] generated by p. In this paper we prove that . We also prove a result that gives information about the structure of a commuting family of operators on a finite Dimensional vector space. From it is derived the well-known theorem of Schur on maximal abelian subalgebras of 𝔤𝔩(n, k).
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FAITHFUL REPRESENTATIONS OF Minimal Dimension OF CURRENT HEISENBERG LIE ALGEBRAS
International Journal of Mathematics, 2009Co-Authors: Leandro Cagliero, Nadina RojasAbstract:Given a Lie algebra
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Faithful representations of Minimal Dimension of current Heisenberg Lie algebras
arXiv: Representation Theory, 2008Co-Authors: Leandro Cagliero, Nadina RojasAbstract:Given a Lie algebra $\mathfrak{g}$ over a field of characteristic zero $k$, let $\mu(\mathfrak{g})=\min\{\dim \pi: \pi\text{is a faithful representation of}\mathfrak{g}\}$. Let $\mathfrak{h}_{m}$ be the Heisenberg Lie algebra of Dimension $2m+1$ over $k$ and let $k[t]$ be the polynomial algebra in one variable. Given $m\in\mathbb{N}$ and $p\in k[t]$, let $\mathfrak{h}_{m,p}=\mathfrak{h}_m\otimes k[t]/(p)$ be the current Lie algebra associated to $\mathfrak{h}_m$ and $k[t]/(p)$, where $(p)$ is the principal ideal in $k[t]$ generated by $p$. In this paper we prove that $ mu(\mathfrak{h}_{m,p}) = m \deg p + \left \lceil 2\sqrt{\deg p} \right\rceil$.
Bruno Zimmermann - One of the best experts on this subject based on the ideXlab platform.
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On Minimal actions of finite simple groups on homology spheres and Euclidean spaces
arXiv: Geometric Topology, 2008Co-Authors: Bruno ZimmermannAbstract:We consider the following problem: for which classes of finite groups, and in particular finite simple groups, does the Minimal Dimension of a faithful, smooth action on a homology sphere coincide with the Minimal Dimension of a faithful, linear action on a sphere? We prove that the two Minimal Dimensions coincide for the linear fractional groups PSL(2,p) as well as for various classes of alternating and symmetric groups. We prove analogous results also for actions on Euclidean spaces.
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On the Minimal Dimension of a homology sphere on which a finite group acts
Mathematical Proceedings of the Cambridge Philosophical Society, 2008Co-Authors: Bruno ZimmermannAbstract:AbstractWe show that the Minimal Dimension of a faithful action of a metacyclic group$\Z_p \rtimes \Z_q$, for primespandq, on a homology sphere coincides with the Minimal Dimension of a faithful linear action on a sphere; as a consequence, we obtain the analogous result for various finite simple groups.