Operator algebras over the p-adic integers

We study p-adic operator algebras, which are nonarchimedean analogues of C^*-algebras. We demonstrate that various classical examples of operator algebras - such as group(oid) algebras - have a nonarchimedean counterpart. The category of p-adic operator algebras exhibits a similar flavor to the category of real and complex C^*-algebras, featuring limits, colimits, tensor products, crossed products and an enveloping construction permitting us to construct p-adic operator algebras from involutive algebras over Zₚ. Finally, we briefly discuss an analogue of topological K-theory for Banach Zₚ-algebras, and compute it in basic examples, like Cuntz algebras and rotation algebras.