English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $k$ be an arbitrary field, $\Lambda$ be a $k$-algebra and $V$ be a$\Lambda$-module. When it exists, the universal deformation ring $R(\Lambda,V)$of $V$ is a $k$-algebra whose local homomorphisms to $R$ parametrize the liftsof $V$ up to $R\otimes_k \Lambda$, where $R$ is any complete, local commutativeNoetherian $k$-algebra with residue field $k$. Symmetric special biserialalgebras, which coincide with Brauer graph algebras, can be viewed asgeneralizing the blocks of finite type $p$-modular group algebras. Bleher andWackwitz classified the universal deformation rings for all modules forsymmetric special biserial algebras with finite representation type. In thispaper, we begin to address the tame case. Specifically, let $\Lambda$ be any1-domestic, symmetric special biserial algebra. By viewing $\Lambda$ asgeneralized Brauer tree algebras and making use of a derived equivalence, weclassify the universal deformation rings for those $\Lambda$-modules $V$ withstable endomorphism ring isomorphic to $k$. The latter is a natural condition,since it guarantees the existence of the universal deformation ring$R(\Lambda,V)$.

Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth