In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries conserved quantities language commutant algebras. particular, start with defined by parts are local, study algebra operators separately commute each part. The models include spin-1/2 Heisenberg model its deformations, types spinless spinful free-fermion models, Hubbard m...

We study the structure of a class of weighted Toeplitz operators and obtain a description of the commutant of each operator in this class. We make some progress towards proving that the only operator in the commutant which is not a scalar multiple of the identity operator and which commutes with a nonzero compact operator is zero. The proof of the main statement relies on a conjecture which is ...

Various theorems on lifting strong commutants of unbounded sub-normal (as well as formally subnormal) operators are proved. It is shown that the strong symmetric commutant of a closed symmetric operator S lifts to the strong commutant of some tight selfadjoint extension of S. Strong symmetric commutants of orthogonal sums of subnormal operators are investigated. Examples of (unbounded) irreduci...

The commutant lifting theorem of Sz.Nagy and Foiaş [22, 21] is a central result in the dilation theory of a single contraction. It states that if T ∈ B(H) is a contraction with isometric dilation V acting on K ⊃ H, and TX = XT , then there is an operator Y with ‖Y ‖ = ‖X‖, V Y = Y V and PHY = XPH. This result is equivalent to Ando’s Theorem that two commuting contractions have a joint (power) d...

An operator is said to be strongly irreducible if its commutant has no nontrivial idempotent. This paper first shows that if an operator is not strongly irreducible then the set of idempotents in its commutant is either finite or uncountable. The second part of the paper focuses on the Jordan block which is a well-known class of irreducible operators, and determines when a Jordan block is stron...

Utilizing the understanding of symmetries in framework commutant algebras, authors introduce here general methods to numerically construct symmetry operators and quantum number sectors. One method uses simultaneous block diagonalization two generic Hamiltonians sectors, while another fact that are frustration-free ground states local superoperators, which leads efficient algorithms. These appli...

A natural first step in the classification of all 'physical' modular invariant partition functions N LR χ L χ * R lies in understanding the commutant of the modular matrices S and T. We begin this paper extending the work of Bauer and Itzykson on the commutant from the SU (N) case they consider to the case where the underlying algebra is any semi-simple Lie algebra (and the levels are arbitrary...

In this note we show that the commutant of a Bol loop of odd order is a subloop.

We show that the commutant lifting theorem for n-tuples of commuting contractions with regular dilations fails to be true. A positive answer is given for operators which ”double intertwine” given n-tuples of contractions. The commutant lifting theorem is one of the most important results of the Sz. Nagy—Foias dilation theory. It is usually stated in the following way: Theorem. Let T and T ′ be ...