For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of BirmanMurakami-Wenzl type QM-algebras, we investigate a structure of its characteristic subalgebra (the subalgebra in which the coefficients of characteristic polynomials take values). We define 3 sets of generating elements of the...

A reductive Lie algebra g is one that can be written C(g) ⊕ [g,g], where C(g) denotes the center of g. Equivalently, for any ideal a, there is another ideal b such that g = a⊕ b. A Cartan subalgebra of g is a subalgebra h that is maximal with respect to being abelian and having ad X being semisimple for all X ∈ h. For a reductive group, h = C(g) ⊕ h′, where h′ is a Cartan subalgebra of the semi...

This paper introduces the concept of subalgebra and discusses some properties subalgebra. We also examine different types ideals how they behave. describe a homomorphism. Finally, we present quotient algebra discuss isomorphism theorems.

We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’1-CA0 over RCA0.

The aim of this article is to obtain more general forms than the papers of Jun et al. 2010 ; Jun et al. in press . The notions of N-subalgebras of types ∈, qk , ∈,∈ ∨qk , and q,∈ ∨qk are introduced, and the concepts of qk-support and ∈ ∨qk-support are also introduced. Several related properties are investigated. Characterizations of N-subalgebra of type ∈,∈ ∨qk are discussed, and conditions for...

The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. We identify a localized subalgebra on which the Zeno dynamics acts by automorphisms. The Zeno dynamics coincides with the modular dynamics of that subalgebra, if an additional assumption is satisfied. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a varia...

In [14] we showed that for each locally finite unary (total) algebra of finite type, its weak subalgebra lattice uniquely determines its (strong) subalgebra lattice. Now we generalize this fact to algebras having also finitely many binary operations (for example, groupoids, semigroups, semilattices). More precisely, we generalize some ideas from [14] to prove: Let A be a locally finite (total) ...