Any non-pure quantum state admits an innnity of non-trivial decom-positions. A recent proposal how to measure the information content of a quantum state with reference to a given subalgebra of operators, singles out some of them, called optimal decompositions, which depend both on the state and on the subalgebra. In this paper we start exploring their main features.

In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras. With this tool, we obtain the dual atomicity of these lattices, and characterize the members of these varieties in which every subalgebra is an intersection of maximal subalgebras. Then, we determine the algebras that have a modular or distributive lattice of suba...

Any non-pure quantum state admits an infinity of non-trivial decompositions. A recent proposal how to measure the information content of a quantum state with reference to a given subalgebra of operators, singles out some of them, called optimal decompositions, which depend both on the state and on the subalgebra. In this paper we start exploring their main features.

We show that every logmodular subalgebra of Mn(C) is unitary equivalent to an algebra of block upper triangular matrices, which was conjectured in [5]. In particular, this shows that every unital contractive representation of a logmodular subalgebra of Mn(C) is automatically completely contractive.

We consider the decoherence free subalgebra which satisfies the minimal condition introduced by Alicki [1]. We show the manifest form of it and relate the subalgebra with the Kraus representation. The arguments also provides a new proof for generalized Lüders theorem [5].

A triangular quantum deformation of osp(2/1) from the classical r-matrix including an odd generator is presented with its full Hopf algebra structure. The deformation maps, twisting element and tensor operators are considered for the deformed osp(2/1). It is also shown that its subalgebra generated by the Borel subalgebra is self-dual.

We study the induction and restriction functor from a Hopf subalgebra of a semisimple Hopf algebra. The image of the induction functor is described when the Hopf subalgebra is normal. In this situation, at the level of characters this image is isomorphic to the image of the restriction functor. A criterion for subcoalgebras to be invariant under the adjoint action is given generalizing Masuoka’...

Recently, Brzezi\'nski, Koenig and K\"ulshammer have introduced the notion of normal exact Borel subalgebra a quasihereditary algebra. They shown that there exists one-to-one correspondence between directed bocses algebras with homological subalgebra. In this short note, we prove every is automatically normal. As corollary, conclude bocs has group-like element. These results simplify K\"ulshamm...