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math.RT2026
Modules and operator rings of Reynolds algebras
Jun He, Xiao-Song Peng, Chenghao Zhang +1
We develop a module theory for weighted Reynolds algebras by constructing an associa?tive ring that records the algebra action and the module operator. The categories of left and r…
math.CT2026
Monoidal structure on Rota-Baxter algebras via augmentation, and free cocycle bialgebras
Li Guo, Yunzhou Xie, Yi Zhang
A tensor product is known for commutative Rota--Baxter algebras through a universal construction, but its underlying algebra need not be the ordinary tensor product an…
math.RA2026
Rota-Baxter operators and factorization of Lie affgebras
JiaJia Han, Abror Khudoyberdiyev, Yunzhou Xie +1
We introduce Rota-Baxter operators on Lie affgebras by an identity independent of the choice of origin and prove that they induce descendant Lie affgebra structures. We establish a…