共查询到20条相似文献,搜索用时 15 毫秒
1.
Certain weak versions of the Shepherdson's condition for open induction in a discretely ordered ring are given, and their relationships to each other and to the underlying group structure of the ring are studied. 相似文献
2.
Jingjing Ma 《Algebra Universalis》2009,62(1):51-61
We construct all the lattice orders on a 2 × 2 triangular matrix algebra over a totally ordered field that make it into a
lattice-ordered algebra. It is shown that every lattice order in which the identity matrix is not positive may be obtained
from a lattice order in which the identity matrix is positive. 相似文献
3.
Fergus Gaines 《Linear and Multilinear Algebra》2013,61(2):95-98
In this note, we show how the algebra of n×n matrices over a field can be generated by a pair of matrices A B, where A is an arbitrary nonscalar matrix and B can be chosen so that there is the maximum degree of linear independence between the higher commutators of B with A. 相似文献
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《Expositiones Mathematicae》2020,38(2):259-270
In the high-energy quantum-physics literature one finds statements such as “matrix algebras converge to the sphere”. Earlier I provided a general setting for understanding such statements, in which the matrix algebras are viewed as compact quantum metric spaces, and convergence is with respect to a quantum Gromov–Hausdorff-type distance. More recently I have dealt with corresponding statements in the literature about vector bundles on spheres and matrix algebras. But physicists want, even more, to treat structures on spheres (and other spaces) such as Dirac operators, Yang–Mills functionals, etc., and they want to approximate these by corresponding structures on matrix algebras. In preparation for understanding what the Dirac operators should be, we determine here what the corresponding “cotangent bundles” should be for the matrix algebras, since it is on them that a “Riemannian metric” must be defined, which is then the information needed to determine a Dirac operator. (In the physics literature there are at least 3 inequivalent suggestions for the Dirac operators.) 相似文献
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7.
In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2,) of complex 2×2 matrices related to the two-sided action ofU(2)×U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation ofGL(2,) and each eigenvalue is expressed as a finite sum involving the MeijerG-functions evaluated at 1 and the Hahn polynomials. 相似文献
8.
D. P. Novikov 《Theoretical and Mathematical Physics》2009,161(2):1485-1496
We show that the Belavin-Polyakov-Zamolodchikov equation of the minimal model of conformal field theory with the central charge
c = 1 for the Virasoro algebra is contained in a system of linear equations that generates the Schlesinger system with 2×2 tmatrices. This generalizes Suleimanov’s result on the Painlevé equations. We consider the properties of the solutions, which
are expressible in terms of the Riemann theta function. 相似文献
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D. V. Bykov 《Theoretical and Mathematical Physics》2010,163(1):496-510
By direct calculation in the classical theory, we derive the central extension of the off-shell symmetry algebra for a string propagating in AdS 4 ×?? 3 . It turns out to be the same as in the case of the AdS 5 ×S 5 string. We consider the choice of the κ-symmetry gauge in detail and also explain how this gauge can be chosen without breaking the bosonic symmetries. 相似文献
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Nguy?n H. V. Hu’ng 《Mathematische Annalen》2012,353(3):827-866
The Dickson–Mùi algebra consists of all invariants in the mod p cohomology of an elementary abelian p-group under the general linear group. It is a module over the Steenrod algebra, A{\mathcal {A}} . We determine explicitly all the A{\mathcal {A}} -module homomorphisms between the (reduced) Dickson–Mùi algebras and all the A{\mathcal {A}} -module automorphisms of the (reduced) Dickson–Mùi algebras. The algebra of all A{\mathcal {A}} -module endomorphisms of the (reduced) Dickson–Mùi algebra is claimed to be isomorphic to a quotient of the polynomial algebra on one indeterminate. We prove that the reduced Dickson–Mùi algebra is atomic in the meaning that if an A{\mathcal {A}} -module endomorphism of the algebra is non-zero on the least positive degree generator, then it is an automorphism. This particularly shows that the reduced Dickson–Mùi algebra is an indecomposable A{\mathcal {A}} -module. The similar results also hold for the odd characteristic Dickson algebras. In particular, the odd characteristic reduced Dickson algebra is atomic and therefore indecomposable as a module over the Steenrod algebra. 相似文献
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15.
Let M
n
denote the algebra of complex n × n matrices and write M for the direct sum of the M
n
. So a typical element of M has the form
x = x1?x2 ??xn ??, x = x_1\oplus x_2 \cdots \oplus x_n \oplus \cdots, 相似文献
16.
G. L. Rybnikov 《Journal of Mathematical Sciences》1992,59(5):1117-1123
Generators of the space of tensor invariants of the Lie algebra Sl2([t]) are constructed. It is proved that the restrictions of a spinor representation of the affine Lie algebra
to
and
form a dual pair. A realization of the fundamental representations of the Lie algebra
is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 137–144, 1989. 相似文献
17.
Xu Kong 《Linear and Multilinear Algebra》2013,61(10):1348-1362
Using rank-1 reduction formula and the vector space spanned by the real rank-1 matrices, we present a different way to show that the maximum possible rank of the 2?×?2?×?2 tensors over the real field is 3. Following, we obtain that the maximum rank of the 2?×?2?×?2?×?2 tensors over the real field is less than or equal to 5 and propose another way to show that the maximum rank of the 2?×?2?×?2?×?2 tensors over the complex field is 4, except one special case. 相似文献
18.
Kris Coolsaet 《Designs, Codes and Cryptography》2013,68(1-3):179-194
As a first step in the classification of nonsingular 2×2×2×2 hypercubes up to equivalence, we resolve the case where the base field is finite and the hypercubes can be written as a product of two 2×2×2 hypercubes. (Nonsingular hypercubes were introduced by D. Knuth in the context of semifields. Where semifields are related to hypercubes of dimension 3, this paper considers the next case, i.e., hypercubes of dimension 4.) We define the notion of ij-rank (with 1 ≤ i < j ≤ 4) and prove that a hypercube is the product of two 2×2×2 hypercubes if and only if its 12-rank is at most 2. We derive a ‘standard form’ for nonsingular 2×2×2×2 hypercubes of 12-rank less than 4 as a first step in the classification of such hypercubes up to equivalence. Our main result states that the equivalence class of a nonsingular 2×2×2×2 hypercube M of 12-rank 2 depends only on the value of an invariant δ 0(M) which derives in a natural way from the Cayley hyperdeterminant det0 M and another polynomial invariant det M of degree 4. As a corollary we prove that the number of equivalence classes is (q + 1)/2 or q/2 depending on whether the order q of the field is odd or even. 相似文献
19.
By using quantum vertex operators we study the invariance of the rank n free-fermion vertex algebra under the action of the group ?∕2? and obtain its minimal generating set. When n = 1, it is well known that this subalgebra is isomorphic to the Virasoro vertex algebra with central charge 1∕2. In the n = 2 case we show that invariant subalgebra is isomorphic to a simple quotient of a certain W-algebra, which we explicitly construct. For n≥3, our approach leads to a rediscovery of the spinor representation of the a?ne vertex algebra associated to the Lie algebra 𝔰𝔬(n) of I. Frenkel. 相似文献
20.
In this paper the generalized factorization for a class of 2×2 piecewise continuous matrix functions on is studied. Using a space transformation the problem is reduced to the generalized factorization of a scalar piecewise continuous function on a contour in the complex plane. Both canonical and non-canonical generalized factorization of the original matrix function are studied.Sponsored by J.N.I.C.T. (Portugal) under grant no. 87422/MATM 相似文献
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