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In this paper, we mainly focus on the Poincare-Birkhoff-Witt (PBW) deformation theory for a class of N-homogeneous algebras; here N >= 2 is an integer, which generalizes the results in [2] and [7]. More precisely, let k be a field...
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In this paper, we mainly focus on the Poincare-Birkhoff-Witt (PBW) deformation theory for a class of N-homogeneous algebras; here N >= 2 is an integer, which generalizes the results in [2] and [7]. More precisely, let k be a field of characteristic zero, V a finite dimensional vector space over k, and A = T(V)/(R) an N-homogeneous algebra (i.e., R subset of V-circle times N) with Tor(A)(3)(k, k) being supported in a single degree d such that d > N. Set F-n := circle plus(0 = 0 and J(n) = 0 for n < N.
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In this paper we consider n-homogeneous C~*-algebras generated by idempotents. We prove that a finitely generated unital n-homogeneous (when n is greater than or equals 2) C~*-algebra A can be generated by a finite set of idempote...
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In this paper we consider n-homogeneous C~*-algebras generated by idempotents. We prove that a finitely generated unital n-homogeneous (when n is greater than or equals 2) C~*-algebra A can be generated by a finite set of idempotents if and only if the algebra A contains at least one nontrivial idempotent.
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Let & frac12;H(n, 2) denote the halved n-cube with vertex set X and let T := T(x(0)) denote the Terwilliger algebra of & frac12;H(n, 2) with respect to a fixed vertex x(0) is an element of & nbsp;X. In this paper, we assume n >=& nbsp;6. We first characteriz...
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Let & frac12;H(n, 2) denote the halved n-cube with vertex set X and let T := T(x(0)) denote the Terwilliger algebra of & frac12;H(n, 2) with respect to a fixed vertex x(0) is an element of & nbsp;X. In this paper, we assume n >=& nbsp;6. We first characterize T by considering the action of the automorphism group of & frac12;H(n, 2) on the set X x X x X. We show that T coincides with the centralizer algebra of the stabilizer of x(0) in the automorphism group, and display three subalgebras of T further. Then we study the homogeneous components of V := C-X, each of which is a nonzero subspace of V spanned by the irreducible T-modules that are isomorphic. We give a computable basis for any homogeneous component of V. Finally, we describe the decomposition of T via its block-diagonalization and give a basis for the center of T by using the above homogeneous components of V. (c) 2021 Elsevier Ltd. All rights reserved.
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We study n-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an n-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from l-and m-i...
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We study n-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an n-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from l-and m-inverse pairs of operators on the individual spaces. This gives a converse to a result of Duggal and Muller (2013), and proves a conjecture of the second named author (2015). Our proof uses techniques from algebraic geometry, which generalize to other relations among operators in a tensor product. We apply this theory to obtain results for n-symmetries in a tensor product as well.
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We consider algebraic bundles over a two-dimensional compact oriented connected manifold. In 1961 J. Fell, J. Tomiyama, M. Takesaki showed that every n-homogeneous C*-algebra is isomorphic to the algebra of all continuous sections...
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We consider algebraic bundles over a two-dimensional compact oriented connected manifold. In 1961 J. Fell, J. Tomiyama, M. Takesaki showed that every n-homogeneous C*-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic bundle. By using this realization we prove in the work that every 2-homogeneous C*-algebra over two-dimensional compact oriented connected manifold can be generated by three idempotents. Such algebra can not be generated by two idempotents.
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We extend Koszul calculus defined on quadratic algebras by Berger et al. (2018) [9] to N-homogeneous algebras for any N >= 2, quadratic algebras corresponding to N = 2. We emphasize that N-homogeneous algebras are considered in fu...
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We extend Koszul calculus defined on quadratic algebras by Berger et al. (2018) [9] to N-homogeneous algebras for any N >= 2, quadratic algebras corresponding to N = 2. We emphasize that N-homogeneous algebras are considered in full generality, with no Koszulity assumption. Koszul cup and cap products are introduced and are reduced to usual cup and cap products if N = 2, but if N > 2, they are defined by very specific expressions. These specific expressions are compatible with the Koszul differentials and provide associative products on classes. There is no associativity in general on chainscochains, suggesting that Koszul cochains should constitute an A(infinity)-algebra, acting as an A(infinity)-bimodule on Koszul chains. (C) 2018 Elsevier Inc. All rights reserved.
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The concepts of solvable and nilpotent Leibniz n-algebra are introduced, and classical results of solvable and nilpotent Lie algebras theory are extended to Leibniz n-algebras category. A homological criterion similar to Stallings...
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The concepts of solvable and nilpotent Leibniz n-algebra are introduced, and classical results of solvable and nilpotent Lie algebras theory are extended to Leibniz n-algebras category. A homological criterion similar to Stallings Theorem for Lie algebras is obtained in Leibniz n-algebras category by means of the homology with trivial coefficients of Leibniz n-algebras.
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We study naturally graded filiform n-Lie algebras. Among these algebras, we distinguish some algebra with the simplest structure that is an analog of the model filiform Lie algebra. We describe the derivations of the algebra and o...
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We study naturally graded filiform n-Lie algebras. Among these algebras, we distinguish some algebra with the simplest structure that is an analog of the model filiform Lie algebra. We describe the derivations of the algebra and obtain the classification of solvable n-Lie algebras whose maximal hyponilpotent ideal coincides with the distinguished naturally graded filiform algebra. Furthermore, we show that these solvable n-Lie algebras possess outer derivations.
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We prove that a connected, countable dense homogeneous space is n-homogeneous for every n, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous spac...
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We prove that a connected, countable dense homogeneous space is n-homogeneous for every n, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers in the negative Problem 136 ofWatson in the Open Problems in Topology Book.
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We discuss the nonstochastic homogenization of nonlinear parabolic differential operators in an abstract setting framed to bridge the gap between periodic and stochastic homogenization theories. Instead of the classical periodicit...
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We discuss the nonstochastic homogenization of nonlinear parabolic differential operators in an abstract setting framed to bridge the gap between periodic and stochastic homogenization theories. Instead of the classical periodicity hypothesis, we have here an abstract assumption covering a great variety of concrete behaviours in both space and time variables, such as the periodicity, the almost periodicity, the convergence at infinity, and others. Our basic approach is the Sigma-convergence method generalizing the well-known two-scale convergence technique. Fundamental homogenization theorems are proved and several concrete examples are worked out, which reveal that homogenization beyond the periodic setting may involve difficulties that are beyond imagination. (c) 2006 Elsevier Ltd. All rights reserved.
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