Antipodes of monoidal decomposition spaces
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
We introduce a notion of antipode for monoidal (complete) decomposition spaces, inducing a notion of weak antipode for their incidence bialgebras. In the connected case, this recovers the usual notion of antipode in Hopf algebras. In the non-connected case, it expresses an inversion principle of more limited scope, but still sufficient to compute the Mobius function as mu = zeta o S, just as in Hopf algebras. At the level of decomposition spaces, the weak antipode takes the form of a formal difference of linear endofunctors S-even - S-odd, and it is a refinement of the general Mobius inversion construction of Galvez-Kock-Tonks, but exploiting the monoidal structure.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 1850081 |
Tidsskrift | Communications in Contemporary Mathematics |
Vol/bind | 22 |
Udgave nummer | 2 |
Antal sider | 15 |
ISSN | 0219-1997 |
DOI | |
Status | Udgivet - mar. 2020 |
Eksternt udgivet | Ja |
ID: 331497757