Tensor products in the category of topological vector spaces are not associative

有限 $C^\u221E$-生成的结合代数与Hopf代数

Finitely $C^\infty$-generated associative and Hopf algebras

本文引入有限C^∞-生成代数（非交换C^∞-微分流形的函数代数），用多项式增长实Banach代数射影极限范畴方法，证明自由C^∞-函数代数结构定理的一般情形，核心结果为有限个该代数的射影张量积仍有限C^∞-生成，还构造了仿射实Hopf代数到有限C^∞-生成Hopf代数的包络函子。

On tensor fractions and tensor products in the category of stereotype spaces

We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with the tensor products in the category $\sf{Ste}$ of stereotype spaces. In particular, we give sufficient conditions under which the identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle $$ holds, where $\odot$ is the injective tensor product in the category $\sf{Ste}$, $\cdot$, the primary tensor product in the category $\sf{LCS}$, and $\vartriangle$, the pseudosaturation operation in the category $…

The representation category of the Woronowicz quantum group S_mu U(d) as a braided tensor C*-category

An abstract characterization of the representation category of the Woronowicz twisted SU(d) group is given, generalizing analogous results known in the classical case