algebrascollection

Algebrascollection is a proposed digital repository and reference framework for algebraic structures. It aims to catalog and describe a wide range of algebras, including associative, commutative, Lie, Jordan, Hopf, and other varieties, along with their defining properties, examples, and interrelations. The goal is to provide a centralized resource for researchers, students, and educators to access standardized information about algebras across different fields such as pure mathematics, representation theory, and mathematical physics.

Entries in algebrascollection are modeled with a consistent data schema. Each item records the name, type, base field, dimension, generators, relations, and canonical presentations, as well as invariants such as growth, homological properties, and representation categories when available. The collection uses a controlled vocabulary and a hierarchical taxonomy to group entries by algebra type, characteristic, and construction method. Cross-references link to classical literature and related algebras, and historical notes document naming variants and prior definitions.

Access is envisioned through a web interface and an application programming interface that allow browsing, advanced search, and data export. The platform promotes community contribution under editorial oversight, with versioning, change logs, and quality checks to ensure reliability. Licensing is set to permit reuse under open licenses where possible, with attribution requirements for non-original content.

Examples in the imagined collection would include finite-dimensional associative algebras, polynomial algebras, Lie algebras over various fields, and fundamental constructs such as matrix algebras, universal enveloping algebras, and simple Lie algebras. The project would interact with existing mathematical databases and computational tools to facilitate analysis, computation, and reproducibility.