Details

Autor(en) / Beteiligte

• Harman, Nate
• Snowden, Andrew

Titel

Ultrahomogeneous tensor spaces

Ist Teil von

• Advances in mathematics (New York. 1965), 2024-05, Vol.443, p.109599, Article 109599

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2024

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• A cubic space is a vector space equipped with a symmetric trilinear form. Using categorical Fraïssé theory, we show that there is a universal ultrahomogeneous cubic space V of countable infinite dimension, which is unique up to isomorphism. The automorphism group G of V is quite large and, in some respects, similar to the infinite orthogonal group. We show that G is a linear-oligomorphic group (a class of groups we introduce), and we determine the algebraic representation theory of G. We also establish some model-theoretic results about V: it is ω-categorical (in a modified sense), and has quantifier elimination (for vectors). Our results are not specific to cubic spaces, and hold for a very general class of tensor spaces; we view these spaces as linear analogs of the relational structures studied in model theory.