The phrase "algebra rank" is correct and usable in written English.
It can be used in mathematical contexts, particularly when discussing the rank of a matrix in linear algebra.
Example: "To determine the algebra rank of the matrix, we need to perform row reduction."
Alternatives: "matrix rank" or "rank in algebra".
Note that the operators L ( m 2 p − 1 m 2 p ) form a maximal abelian subalgebra which proves that the system algebra has rank d.
Let ( V, ∘ ) be an n-dimensional Euclidean Jordan algebra with rank r equipped with the standard inner product 〈 x, s 〉 = tr ( x ∘ s ).
Using a similar argument as in the proof of Proposition 53, we conclude that the operators L ( m 2 p − 1 m 2 p ) together with the operator L ( ∏ p = 1 d m 2 p − 1 m p ) form a maximal abelian subalgebra which proves that the system algebra has rank d + 1.
These algebras, which generalise the analytic Toeplitz algebras of rank 2 graphs with a single vertex, are classified up to isometric isomorphism in terms of the matrix u.
Other Nichols algebras of rank 2 were presented in [27, 45, 53].
We list all compact, simple Lie algebras of rank k : = d − 1 ≥ 4 : su ( k + 1 ) has dimension k 2 + 2 k, so ( 2 k + 1 ) has dimension 2 k 2 + k, sp ( k ) has dimension 2 k 2 + k, so ( 2 k ) has dimension 2 k 2 − k, as well as the exceptional ones.
A triangular UHF algebra (TUHF) of rank (pn) is any Banach algebra that is isometrically isomorphic to the Banach algebra inductive limit T = limn → ∞(Tpn; σ Pm).
LetAbe a simple unital AT algebra of real rank zero such that it has a unique tracial stateτandK1(A) is neither 0 norZ.
Let ( V, ∘ ) be an n-dimensional Euclidean Jordan algebra (EJA) with rank r equipped with the standard inner product 〈 x, s 〉 = tr ( x ∘ s ), and K be the corresponding symmetric cone.
Furthermore we construct such anαwith the Rohlin property, which is defined in Kishimoto (Comm. Math. Phys.179(1996), 599 622), in this case the crossed productA×αRis a simple AT algebra of real rank zero.
