Materializing Morality

This chapter examines the salt merchants’ role in constructing chastity arches—stone structures honoring women who maintained chaste widowhood—in She county in Huizhou. In the High Qing era, the Manchu court systematically patronized the construction of monumental objects, such as stone arches, with the dual object of inculcating Confucian morality in their illiterate subjects and displaying their imperial legitimacy. The Huizhou salt merchants, seeing an opportunity to expand their influence, devoted themselves to chastity arch construction in the local community of Huizhou, thus publicizing the virtuous deeds that the court rewarded. While these merchants used their economic prowess to participate in the state’s cultivation project, their financial support of these arches was itself a product of the court’s salt monopoly policies. At the same time, these monuments gave these wealthy businessmen the opportunity to bolster their reputations, display their wealth, and lay claim to legitimate dominance in local society.

CLIFFORD MODULES AND SYMMETRIES OF TOPOLOGICAL INSULATORS

We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of real irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland–Zirnbauer symmetry classes of fermion systems and the ten Morita equivalence classes of real and complex Clifford algebras. The antiunitary operators, which occur in seven classes, are projectively represented in the Nambu space by unitary "chiral symmetries". The space of gapped symmetric hamiltonians is homotopically equivalent to the product of classifying spaces indexed by the dual object of the group of unitary symmetries.

Ont-entropy and variational principle for the spectral radii of transfer and weighted shift operators

The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations and the principal results have been achieved in the situation when the dynamical system is either reversible or a topological Markov chain. As the main summands, these principles contain the integrals over invariant measures and the Kolmogorov–Sinai entropy. In the paper we derive the variational principle for anarbitrarydynamical system. It gives the explicit description of the Legendre dual object to the spectral potential. It is shown that in general this principle contains not the Kolmogorov–Sinai entropy but a new invariant of entropy type—thet-entropy.

GAUGE-EQUIVARIANT HILBERT BIMODULES AND CROSSED PRODUCTS BY ENDOMORPHISMS

C*-endomorphisms arising from superselection structures with nontrivial center define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz–Pimsner algebra of a vector bundle having the above-mentioned rank, first Chern class and can be used to construct a duality for abstract (nonsymmetric) tensor categories versus group bundles acting on (nonsymmetric) Hilbert bimodules. Existence and unicity of the dual object (i.e. the 'gauge' group bundle) are not ensured: we give a description of this phenomenon in terms of a certain moduli space associated with the given endomorphism. The above-mentioned Hilbert bimodules are noncommutative analogs of gauge-equivariant vector bundles in the sense of Nistor–Troitsky.