Abstract
We compute the generator rank of a subhomogeneous
$C^*\!$
-algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representations ...of a fixed dimension. We deduce that every
$\mathcal {Z}$
-stable approximately subhomogeneous algebra has generator rank one, which means that a generic element in such an algebra is a generator.
This leads to a strong solution of the generator problem for classifiable, simple, nuclear
$C^*\!$
-algebras: a generic element in each such algebra is a generator. Examples of Villadsen show that this is not the case for all separable, simple, nuclear
$C^*\!$
-algebras.
In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB=C, and present the general solution expression when the solvability ...conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX=C and XB=C. Finally, we provide a numerical example to demonstrate the findings of this paper.
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In this paper, for each commutative and integral quantale, we give the stratified Sierpinski $L$-algebraic closure space and a sobrification of stratified $L$-algebraic closure spaces. Furthermore, ...we show that $\bf{S}$$L$-$\bf{AC}_0$---the category of stratified $S_0$-$L$-algebraic closure spaces is epireflective in $\bf{S}$$L$-$\bf{AC}$---the category of stratified $L$-algebraic closure spaces, and $\bf{Sob}$$L$-$\bf{AC}$---the category of sober $L$-algebraic closure spaces is epireflective and $\mathcal{E}$-firm epireflective in the category $\bf{S}$$L$-$\bf{AC}_0$.
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Some of the operator product expansions (OPEs) between the lowest SO(4) singlet higher spin-2 multiplet of spins Formula omitted in an extension of the large Formula omitted (non)linear ...superconformal algebra were constructed in the Formula omitted superconformal coset Formula omitted theory with Formula omitted previously. In this paper, by rewriting the above OPEs with Formula omitted, the remaining undetermined OPEs are completely determined. There exist additional SO(4) singlet higher spin-2 multiplet, six SO(4) adjoint higher spin-3 multiplets, four SO(4) vector higher spin- Formula omitted multiplets, SO(4) singlet higher spin-4 multiplet and four SO(4) vector higher spin- Formula omitted multiplets in the right hand side of these OPEs. Furthermore, by introducing the arbitrary coefficients in front of the composite fields in the right hand sides of the above complete 136 OPEs, the complete structures of the above OPEs are obtained by using various Jacobi identities for generic N. Finally, we describe them as one single Formula omitted super OPE between the above lowest SO(4) singlet higher spin-2 multiplet in the Formula omitted superspace.
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In this paper, we consider the T-space structure of the relatively free Grassmann algebra F.sup.(3) without unity over an infinite field of prime and zero characteristic. Our work is focused on ...T-spaces W.sub.n generated by all so-called n-words. A question about connections between W.sub.r and W.sub.n for different natural numbers r and n is investigated. The proved theorem on these connections allows us to construct the diagrams of inclusions, which, to some extent, clarify the structure of the algebra: the basic T-spaces produce infinite strictly descending chains of inclusions in the algebra F.sup.(3).
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, skew-symmetric biderivations of the affine-Virasoro algebra of type A1 are presented. More precisely, we prove that every skew-symmetric biderivation is an inner biderivation. As an ...application, we characterize the forms of the linear commuting maps on the affine-Virasoro algebra of type A1.
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In this paper, we consider the T-space structure of the relatively free Grassmann algebra F.sup.(3) without unity over an infinite field of prime and zero characteristic. Our work is focused on ...T-spaces W.sub.n generated by all n-words. A question about connections between W.sub.r and W.sub.n for different natural numbers r and n is investigated. The proved theorem on these connections allows us to construct the diagrams of inclusions that, to some extent, clarify the structure of the algebra: the basic T-spaces produce infinite strictly descending chains of inclusions in the algebra F.sup.(3).
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We present a characterization of the Lie (Jordan) sigma-centralizers of triangular algebras. More precisely, it is proved that, under certain conditions, every Lie sigma-centralizer of a triangular ...algebra can be represented as the sum of a sigma-centralizer and a central-valued mapping. It is also shown that every Jordan sigma-centralizer of a triangular algebra is a sigma-centralizer.
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