The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

Proof theory for lattice-ordered groups

Proof-theoretic methods are developed and exploited to establish properties of the variety of lattice-ordered groups. In particular, a hypersequent calculus with a cut rule is used to provide an alternative syntactic proof of the generation of the variety by the lattice-ordered group of automorphisms of the real number chain. Completeness is also established for an analytic (cut-free) hypersequent calculus using cut elimination and it is proved that the equational theory of the variety is co-NP complete.

The Impact of Relationship Conflict on subjective Family Firm Valuation

The present paper empirically investigates the impact of family relationship conflict on subjective firm valuation by family firm owner managers. Drawing on the emerging socioemotional wealth perspective of corporate ownership, we find a U-shaped relationship between relationship conflict inside the family firm and subjective family firm valuation. This finding suggests that negatively valenced emotions induced by the conflict, at low levels of conflict, lead to emotion congruent withdrawal behavior and hence lower valuation. With conflicts gaining in fervor and severity, owner-managers start endowing and pricing sunk costs related to the conflict. This finding suggests that emotions do indeed have spill-over effects on monetary value perceptions and that negatively valenced emotions induced by relationship conflict are not linearly appraised. Rather, to understand the impact of negative emotions on corporate ownership appraisal and attachment it is required to reconcile the emotion congruency with the prospect theory perspective.