NON-AFFINE HOPF ALGEBRA DOMAINS OF GELFAND–KIRILLOV DIMENSION TWO
Abstract We classify all non-affine Hopf algebras H over an algebraically closed field k of characteristic zero that are integral domains of Gelfand–Kirillov dimension two and satisfy the condition Ext 1 H ( k , k ) ≠ 0. The affine ones were classified by the authors in 2010 (Goodearl and Zhang, J. Algebra 324 (2010), 3131–3168).
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10056143
Journal Name:
Glasgow Mathematical Journal
Volume:
59
Issue:
03
Page Range or eLocation-ID:
563 to 593
ISSN:
0017-0895
2. ABSTRACT A search of the first Data Release of the VISTA Variables in the Via Lactea (VVV) Survey discovered the exceptionally red transient VVV-WIT-01 (H − Ks = 5.2). It peaked before March 2010, then faded by ∼9.5 mag over the following 2 yr. The 1.6–22 μm spectral energy distribution in March 2010 was well fit by a highly obscured blackbody with T ∼ 1000 K and $A_{K_s} \sim 6.6$ mag. The source is projected against the Infrared Dark Cloud (IRDC) SDC G331.062−0.294. The chance projection probability is small for any single event (p ≈ 0.01–0.02), which suggests a physical association, e.g. a collision between low mass protostars. However, blackbody emission at T ∼ 1000 K is common in classical novae (especially CO novae) at the infrared peak in the light curve due to condensation of dust ∼30–60 d after the explosion. Radio follow-up with the Australia Telescope Compact Array detected a fading continuum source with properties consistent with a classical nova but probably inconsistent with colliding protostars. Considering all VVV transients that could have been projected against a catalogued IRDC raises the probability of a chance association to p = 0.13–0.24. After weighing several options, it appears likely that VVV-WIT-01 was a classical nova event locatedmore »