In the lattice theory the tensor product A⊗B is naturally defined on (0,∨)−semilattices. In general, when restricted to lattices this construction will not yield a lattice. However, if the tensor product A ⊗ B is capped, then A⊗B is a lattice. It is stated as an open problem in [4] whether the converse is true. In the present paper we prove that it is not so, that is, there are bounded lattices...

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Topology played an important role in physics research during the last few decades. In particular, quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal interesting but have not been measured non-Abelian systems. Here, we use a four-qubit system superconducting circuits to construct degenerate Hamiltonian with parametri...

We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the “isotopic” vector and the stress tensor currents of spins 1 and 2 respectively, we explain this diffe...

In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number ζ an abelian artinian category FS. We call its objects finite factorizable sheaves. They are certain infinite collections of perverse sheaves on configuration spaces, subject to a compatibility (”factorization”) and finiteness conditions. In Chapter 2 the tensor structure on FS is defined using funct...

In O(3) symmetry electrodynamics the field tensor is governed by a nonAbelian Stokes Theorem, as in any non-Abelian gauge theory. The comments on the B component of this field tensor by Hunter in this Issue address B as if it were a U(1) symmetry field, governed by the ordinary Stokes Theorem, and are therefore sequentially erroneous, because there is a basic misunderstanding of the nature of O...