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651.
In a biFrobenius algebra H, in particular in the case that H is a finite dimensional Hopf algebra, the antipode 𝒮:H → H can be decomposed as 𝒮 = tc ○ cφ where cφ:H → H* and tc:H* → H are the Frobenius and coFrobenius isomorphisms. We use this decomposition to present an easy proof of Radford's formula for 𝒮4. Then, in the case that the map 𝒮 satisfies the additional condition that 𝒮 id = id 𝒮 = u ?, we prove the trace formula tr(𝒮2) = ?(t)φ(1). We finish by applying the above results to study the semisimplicity and cosemisimplicity of H. 相似文献
652.
Cobalanced extensions of torsion-free modules by torsion modules over domains are investigated. As in the case of Abelian Groups, these sequences will split if and only if the torsion-free module is a pure submodule of a vector module. Unlike this case, even the torsion-free modules of finite rank need not be locally completely decomposable. For 1-dimensional Noetherian domains, necessary and sufficient conditions are given for that to be true. 相似文献
653.
Carl D. Meyer 《Linear and Multilinear Algebra》2013,61(7):1332-1336
654.
AbstractIn various normed spaces we answer the question of when a given isometry is a square of some isometry. In particular, we consider (real and complex) matrix spaces equipped with unitarily invariant norms and unitary congruence invariant norms, as well as some infinite dimensional spaces illustrating the difference between finite and infinite dimensions. 相似文献
655.
656.
657.
We give a presentation for the degenerate Ringel-Hall algebras of type B by studying the corresponding generic extension monoid algebras.As an application,it is shown that the degenerate Ringel-Hall algebras of type B admit multiplicative bases. 相似文献
658.
Let k be an algebraically closed field of characteristic zero.This paper proves that semisimple Hopf algebras over k of dimension 66,70 and 78 are of Frobenius type. 相似文献
659.
We introduce the notion of τ‐like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω‐like means that every element has finitely many predecessors, while being ζ‐like means that every interval is finite. We consider statements of the form “any τ‐like partial order has a τ‐like linear extension” and “any τ‐like partial order is embeddable into τ” (when τ is ζ this result appears to be new). Working in the framework of reverse mathematics, we show that these statements are equivalent either to $\mathsf {B}{\Sigma }^{0}_{2}$ or to $\mathsf {ACA}_0$ over the usual base system $\mathsf {RCA}_0$. 相似文献
660.
《Expositiones Mathematicae》2020,38(1):60-90
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the properties of dissipative relations are proven. Finally, we deal with the spectral properties of dissipative extensions of dissipative relations and provide results concerning particular realizations of this general setting. 相似文献