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1.
For the complex Clifford algebra (p, q) of dimension n = p + q we define a Hermitian scalar product. This scalar product depends on the signature (p, q) of Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With the aid of Hermitian idempotents we suggest
a new construction of, so called, normal matrix representations of Clifford algebra elements. These representations take into
account the structure of unitary space on Clifford algebra.
The work of N.M. is supported in part by the Russian President’s grant NSh-6705.2006.1. 相似文献
2.
S. Ulrych 《Advances in Applied Clifford Algebras》2008,18(1):93-114
The representations of Clifford algebras and their involutions and anti-involutions are fully investigated since decades.
However, these representations do sometimes not comply with usual conventions within physics. A few simple examples are presented,
which point out that the hyperbolic numbers can close this gap.
相似文献
3.
In this paper we construct the matrix subalgebras ${L_{r,s}(\mathbb{R})}$ of the real matrix algebra ${M_{2^{r+s}} (\mathbb{R})}$ when 2 ≤ r + s ≤ 3 and we show that each ${L_{r,s}(\mathbb{R})}$ is isomorphic to the real Clifford algebra ${\mathcal{C} \ell_{r,s}}$ . In particular, we prove that the algebras ${L_{r,s}(\mathbb{R})}$ can be induced from ${L_{0,n}(\mathbb{R})}$ when 2 ≤ r + s = n ≤ 3 by deforming vector generators of ${L_{0,n}(\mathbb{R})}$ to multiply the specific diagonal matrices. Also, we construct two subalgebras ${T_4(\mathbb{C})}$ and ${T_2(\mathbb{H})}$ of matrix algebras ${M_4(\mathbb{C})}$ and ${M_2(\mathbb{H})}$ , respectively, which are both isomorphic to the Clifford algebra ${\mathcal{C} \ell_{0,3}}$ , and apply them to obtain the properties related to the Clifford group Γ0,3. 相似文献
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Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
X ? *\Bbb CX \rightarrow {}{^{\ast}{\Bbb C}}
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
Mw(X)/M0(X){\cal M}_{\omega}(X)/{\cal M}_0(X)
, for certain external subspaces
M0(X), Mw(X){\cal M}_0(X), {\cal M}_{\omega}(X)
of the hyperfinite dimensional Banach space
*\Bbb CX{}{^{\ast}{\Bbb C}}^X
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
Mw(G)/M0(G){\cal M}_{\omega}(G)/{\cal M}_0(G)
are isometrically isomorphic as Banach algebras. 相似文献
6.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
, for certain external subspaces
of the hyperfinite dimensional Banach space
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
are isometrically isomorphic as Banach algebras.
Research of both authors supported by a grant by VEGA – Scientific Grant Agency of Slovak Republic. 相似文献
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清楚地刻画出有限和由无限可数个基本元生成的Boole代数中极大滤子的具体结构,在全体极大滤子之集上通过自然的方式引入一种紧致的Hausdorff拓扑,证明了当Boole代数可由无限可数个基本元生成时所得的拓扑空间与Cantor三分集同胚. 相似文献
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Let G be a compact group, H a closed subgroup of G and let m be the normalized G-invariant measure on the homogeneous space G / H obtained from Weil’s formula. In this article, for a given Young function \(\varphi \), we give a new class of Banach convolution algebras on homogeneous spaces of compact groups by introducing a convolution and an involution on the Orlicz space \(L^\varphi (G/H, m)\). Finally, a class of linear representations of this class of Banach convolution algebras is presented. 相似文献
11.
Cristina Balderrama Antonio Di Teodoro Adrian Infante 《Advances in Applied Clifford Algebras》2013,23(4):793-813
In recent years, the integral representation problems have been studied in many context and generalities. For example, for the monogenic and meta functions in some Clifford type algebras, see [10, 11]. In this paper we construct a Cauchy-Pompeiu type formula for meta-monogenic operator of order ${n, (D-\lambda)^n, \lambda \in \mathbb{R}}$ , and its conjugate ${(\overline{D} - \lambda)^n}$ in a Clifford algebra depending on parameters ${\mathcal{A}_n(2, \alpha_j, \gamma_{ij})}$ . Using these explicit representation formula of Cauchy-Pompeiu type we will show some applications. 相似文献
12.
There are continuum many quasivarieties of Cantor algebras having an ω-independent quasiequational basis but no independent quasiequational basis whose intersection does have an independent quasiequational basis. 相似文献
13.
本文证明了Cantor集C上所有拓扑共轭于(单边的)有限型子移位的连续自映射的集合在H中稠密,此外C上每个拓扑传递(混合)映射均可被拓扑共轭于有限型子移位的拓仆传递(混合)映射一致逼近. 相似文献
14.
N. G. Marchuk 《Russian Mathematics (Iz VUZ)》2018,62(11):23-27
Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford algebras is closed with respect to the tensor product. 相似文献
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Yi Ming Zou 《Advances in Applied Clifford Algebras》2009,19(1):147-153
The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers
are investigated.
相似文献
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Yunhe Sheng 《Algebras and Representation Theory》2012,15(6):1081-1098
In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application. 相似文献
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