$k$-theoryandhomology;cyclichomologyandcohomology $k$-theoryandoperatoralgebras 13f3514b0516e4016t0519k5619d5522e4658b3453c2458j42 14a2218d5019k3519l4719l5020f1046l5553d5558b3481r60 16t0516t1016s4016t3017b3517b3718d1018c1519a22 16w3016t0517b3718d1019d2320g42 algebraicgeometry algebraictopology algebrasforatriple analysisonmanifolds arithmeticringsandotherspecialrings associativeringsandalgebras bialgebras braidedcategories burnsideandrepresentationrings categoriesandtheories categorieswithstructure categorytheory;homologicalalgebra commutativealgebra commutativerings congresses connectionswithcombinatorics connectionswithlogicandautomata contactgeometry cyclic deformationquantization differentialgeometry dihedral equivariant$k$-theory foundations frobeniusinduction functionalanalysis globalanalysis globalanalysis(mathematics) globaldifferentialgeometry grothendieckgroupsand$k_0$ groupsandalgebrasinquantumtheory grouptheoryandgeneralizations higheralgebraic$k$-theory homologicalmethods homologyandderivedfunctorsfortriples hopfalgebras hopfalgebrasandtheirapplications indextheory infinite-dimensionalmanifolds kasparovtheory($kk$-theory) liealgebrasandliesuperalgebras liegroups linearalgebraicgroupsandrelatedtopics localtheory monadortriad) monoidalcategories(=multiplicativecategories) nonassociativeringsandalgebras noncommutativealgebraicgeometry noncommutativealgebras noncommutativedynamicalsystems noncommutativegeometry noncommutativegeometry(àlaconnes) noncommutativeglobalanalysis noncommutativeresidues operads otherdecisionproblems partialdifferentialequationsonmanifolds;differentialoperators quantumgroups(quantizedenvelopingalgebras)andrelateddeformations quantumgroups(quantizedfunctionalgebras)andtheirrepresentations quantumgroupsandrelatedtopics quantumtheory rigidityresults ringsandalgebrasarisingundervariousconstructions selfadjointoperatoralgebras($c^*$-algebras semisimpleliegroupsandtheirrepresentations singularities smashproductsofgeneralhopfactions specialaspectsofinfiniteorfinitegroups starproducts symmetricmonoidalcategories symplecticgeometry tensorfields topological$k$-theory topologicalgroups triples(=standardconstruction twisted$k$-theory;differential$k$-theory universalenveloping(super)algebras vonneumann($w^*$-)algebras wittvectorsandrelatedrings wordproblems