B. Tsirelson

Graded algebras and subproduct systems: dimension two

Recent works

Boris Tsirelson,
"Graded algebras and subproduct systems: dimension two."
Available online (free of charge) from e-print archive (USA):
or its Israeli mirror:

A research eprint, 21 pages, bibl. 7 refs.

Objects dual to graded algebras are subproduct systems of linear spaces, a purely algebraic counterpart of a notion introduced recently in the context of noncommutative dynamics (Shalit and Solel, Bhat and Mukherjee). A complete classification of these objects in the lowest nontrivial dimension is given in this work, triggered by a question of Bhat.

  1. Definition and theorem.
  2. Main lemma.
  3. Two tensor factors.
  4. Three tensor factors.
  5. On graded algebras and their morphisms.
  6. Proof of the theorem.
  7. Classification.
  8. Appendix: calculating determinants.
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