{
  "abstract": "For any finite-dimensional algebra $A$ over an algebraically closed field, we prove that if $A$ is $E$-infinite, then the Second brick-Brauer-Thrall Conjecture holds for $A$. In fact, we show that if there is a rational ray outside the $τ$-tilting fan of $A$, then $A$ admits an infinite family of $θ$-stable bricks of dimension $d$, for some positive integer $d$ and weight $θ$. To show our main result, from any $τ$-regular component of $A$ with no dense orbit, we obtain a brick component that also has no dense orbit and whose points in general position are $θ$-stable modules for a given weight $θ$. As an important consequence, we conclude that $A$ is stably-discrete (also called multiplicity-free) if and only if $A$ is $E$-finite. Moreover, we prove that Demonet's (lattice point) Conjecture implies the stable Second brick-Brauer-Thrall Conjecture. For $E$-infinite algebras, our results settle several open conjectures. Together with our earlier work and recent developments, this leads to important reductions in the study of some challenging open problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31417",
  "author_total": 2,
  "authors": [
    {
      "name": "Kaveh Mousavand"
    },
    {
      "name": "Charles Paquette"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xhbdyjz96nnd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31417",
  "fulltext_url": null,
  "id": "1xhbdyjz96nnd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31417",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214620632",
  "pdf_url": "https://arxiv.org/pdf/2609.31417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xhbdyjz96nnd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Proof of the Second brick-Brauer-Thrall Conjecture for $E$-infinite algebras",
  "title_text": "A Proof of the Second brick-Brauer-Thrall Conjecture for E-infinite algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/1xhbdyjz96nnd",
  "venue": "arXiv",
  "versions": []
}