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BlockFormControl Block-Form Control of Linear Time-lnvariant Discrete-Time Systems Defined over Commutative Rings E.
[ij][kl] – [kl][ij] = 0 (ℰn is in some sense braided) Dimensionality • ℰn‘s generator set grows as n2 • |ℰn|’s growth is dramatic (qualitatively exponential, quantitatively unknown)2,3 • Closed formulas for the Hilbert series of ℰn (ℋn(q)) are known to be the product of q-numbers for n≤51 • ℋ6(q) cannot be written as the sum of q-numbers1 Commutative Quotients • Define ℰnab to be the subalgebra generated by stipulating4 [ij][kl] = [kl][ij] • This imposes commutativity on the algebra, greatly simplifying its