Coverings of graded pointed Hopf algebras

We introduce the concept of a covering of a graded pointed Hopf algebra. The theory developed shows that coverings of a bosonized Nichols algebra can be concretely expressed by biproducts using a quotient of the universal coalgebra covering group of the Nichols algebra. If there are enough quadratic relations, the universal coalgebra covering is given by the bosonization by the enveloping group of the underlying rack.Comment: to appear in J. of Algebr

Centers of generic algebras with involution

AbstractLet F be an infinite field of characteristic different from 2. Let n be a positive integer, and let V=Mn(F)⊕Mn(F). The projective symplectic and orthogonal groups, PSpn and POn, act on V by simultaneous conjugation. Results of Procesi and Rowen have shown that F(V)PSpn and F(V)POn are the centers of the generic division algebras with symplectic and orthogonal involutions, respectively. Saltman has shown that F(V)PSpn and F(V)POn are stably isomorphic over F for all n even, and that for all n odd F(V)POn is stably rational over F. Saltman has also shown that for all n for which the highest power of 2 dividing n is less than 8, F(V)PSpn and therefore F(V)POn are stably rational over F. We show that the result is also true for all n for which the highest power of 2 dividing n is 8

Identifying the Nature and Value of Expected Merger Synergies

Using a large sample of post-2001 mergers, we show that three components of targets’ intellectual property account for 25% to 33% of merger value creation. In particular, we show that R&D, Technology, and Trademarks generate greater synergies than acquired net tangible assets and goodwill. We also find that acquiring targets’ customer bases is associated with lower synergies and that acquirers overpay for goodwill. Our findings are robust to using conventional and novel wealth effect estimates. They suggest that information about the economic value of acquired assets drawn from price allocation disclosures enables researchers to simultaneously study multiple sources of synergy

The diminished effect of index rebalances

The author revisits the strategy of trading S&P 500 index re-compositions under the pre- and post-crisis financial environments, proving that the return structure has significantly changed. The results show for the first time, that there are currently no tradable abnormal returns between announcement and event dates in the post-crisis sample period, indicating smoother rebalancing mechanisms by bank’s client facing desks and better services for passive end-investors. The newly added firms inflate the S&P 500 index by less than 10 basis points per year. The results could be attributed to improved execution algorithms used by the banks, and potentially to the new regulatory reforms in the sector, which prevents financial institutions from taking large trading positions with their balance sheets

The fundamental group of a Hopf linear category

We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf linear categories over a finite group. We compare this invariant to the fundamental group of the underlying linear category, and we compute those groups for families of examples.Comment: Computations of the fundamental group of some Hopf algebras are added. The relation with the fundamental group of the underlying associative structure is now considered. We also analyse the situation when universal covers and/or gradings exist. Dedicated to Eduardo N. Marcos for his 60th birthday. 24 page