## B. Tsirelson | ## Graded algebras and subproduct systems: dimension two | ## Recent works |

Boris Tsirelson,

"Graded algebras and subproduct systems: dimension two."

arXiv:0905.4418.

Available online (free of charge) from e-print archive (USA):

arXiv.org/abs/0905.4418/

or its Israeli mirror:

il.arXiv.org/abs/0905.4418/

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.

- Definition and theorem.
- Main lemma.
- Two tensor factors.
- Three tensor factors.
- On graded algebras and their morphisms.
- Proof of the theorem.
- Classification.
- Appendix: calculating determinants.

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