5 papers · 1 filter
Orthonormal bases for higher Hilbert spaces
Giovanni Ferrer, Brett Hungar, David Penneys +1
In our previous article [arxiv:2410.05120], we introduced the notion of a finite dimensional 3-Hilbert space, categorifying Baez's 2-Hilbert spaces. In this article, by further cat…
The many faces of higher Hilbert spaces
Giovanni Ferrer, Lukas Müller, David Penneys +1
Finite-dimensional operator algebras can be viewed as , , or -algebras, leading to different notions for their categories of modules and c…
Rigidity of non-negligible objects of moderate growth in braided categories
Pavel Etingof, David Penneys
Let be a field, and let be a Cauchy complete -linear braided category with finite dimensional morphism spaces and . We call an indecompos…
Manifestly unitary higher Hilbert spaces
Quan Chen, Giovanni Ferrer, Brett Hungar +2
Higher idempotent completion gives a formal inductive construction of the -category of finite dimensional -vector spaces starting with the complex numbers. We propose a manif…
Unitary anchored planar algebras
André Henriques, David Penneys, James Tener
In our previous article [arXiv:1607.06041], we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the…