Maximilian Kaipel

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20242026

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math.RT2026

Exceptional versus $I ¨ $ -exceptional sequences for the Auslander algebra of $K [x] / (x^{t})$

Maximilian Kaipel

For $A_{t}$ , the Auslander algebra of $K [x] / (x^{t})$ , it is shown that every complete exceptional sequence of $A_{t}$ -modules is a complete $I ¨ $ -exceptional sequence.…

math.RT2026

Classifying Nakayama algebras with a braid group action on $I ¨ $ -exceptional sequences

Maximilian Kaipel, HÃ¥vard Utne Terland

We characterise those basic and connected Nakayama algebras $I^$ for which the mutation of $I ¨ $ -exceptional sequences respects the braid group relations. We show that this is the c…

math.RT2025

Bricks and $I ¨ $ -tilting theory under base field extensions

Erlend D. BÃ¸rve, Eric J. Hanson, Maximilian Kaipel

Let $K : k$ be a field extension and let $I^$ be a finite-dimensional $k$ -algebra. We investigate the relationship between $I^$ and $I^_{K} = I^ \otimes_{k} K$ with particular emphasis on…

math.RT2025

$I ¨ $ -cluster morphism categories of factor algebras

Maximilian Kaipel

We take a novel lattice-theoretic approach to the $I ¨ $ -cluster morphism category $T (A)$ of a finite-dimensional algebra $A$ and define the category via the lattice of to…

math.RT2025

Mutating ordered $I ¨ $ -rigid modules with applications to Nakayama algebras

Aslak B. Buan, Maximilian Kaipel, HÃ¥vard U. Terland

A mutation operation for $I ¨ $ -exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of m…

math.RT2024

The category of a partitioned fan

Maximilian Kaipel

In this paper, we introduce the notion of an admissible partition of a simplicial polyhedral fan and define the category of a partitioned fan as a generalisation of the $I ¨ $ -cluste…

Exceptional versus I¨-exceptional sequences for the Auslander algebra of K[x]/(xt)

Classifying Nakayama algebras with a braid group action on I¨-exceptional sequences

Bricks and I¨-tilting theory under base field extensions

I¨-cluster morphism categories of factor algebras

Mutating ordered I¨-rigid modules with applications to Nakayama algebras

The category of a partitioned fan

Exceptional versus $I ¨ $ -exceptional sequences for the Auslander algebra of $K [x] / (x^{t})$

Classifying Nakayama algebras with a braid group action on $I ¨ $ -exceptional sequences

Bricks and $I ¨ $ -tilting theory under base field extensions

$I ¨ $ -cluster morphism categories of factor algebras

Mutating ordered $I ¨ $ -rigid modules with applications to Nakayama algebras