3 results
q-deformed rational numbers and the 2-Calabi–Yau category of type
$A_{2}$
- Part of
- Asilata Bapat, Louis Becker, Anthony M. Licata
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- Journal:
- Forum of Mathematics, Sigma / Volume 11 / 2023
- Published online by Cambridge University Press:
- 12 June 2023, e47
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- Article
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We describe a family of compactifications of the space of Bridgeland stability conditions of a triangulated category, following earlier work by Bapat, Deopurkar and Licata. We particularly consider the case of the 2-Calabi–Yau category of the
$A_2$ quiver. The compactification is the closure of an embedding (depending on q) of the stability space into an infinite-dimensional projective space. In the
$A_2$ case, the three-strand braid group
$B_3$ acts on this closure. We describe two distinguished braid group orbits in the boundary, points of which can be identified with certain rational functions in q. Points in one of the orbits are exactly the q-deformed rational numbers recently introduced by Morier-Genoud and Ovsienko, while the other orbit gives a new q-deformation of the rational numbers. Specialising q to a positive real number, we obtain a complete description of the boundary of the compactification.
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. 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- By Dag Aarsland, Adrià Arboix, Carlos Bazán, James T. Becker, Sylvie Belleville, Kevin M. Biglan, Sandra E. Black, Mariana Blanco, Rémi W. Bouchard, Bruce J. Brew, David J. Burn, Leonardo Caixeta, Richard Camicioli, Paulo Caramelli, Neil Cashman, Nicholas W. S. Davies, Yan Deschaintre, Rachel S. Doody, Bruno Dubois, Uwe Ehrt, Stephane Epelbaum, Ryan V. V. Evans, Joseph M. Ferrara, Bruno Franchi, Morris Freedman, Anders Gade, Serge Gauthier, Marta Grau-Olivares, Matthew E. Growdon, Will Guest, Marie Christie Guiot, Shahul Hameed, Mirna Lie Hosogi-Senaha, Ging-Yuek Robin Hsiung, Masamichi Ikawa, Rajive Jassal, Vesna Jelic, Peter Johannsen, Edward S. Johnson, Mary M. Kenan, Bert-Jan Kerklaan, Benjamin Lam, Gabriel C. Léger, Gabriel Leonard, Emilie Lepage, Irene Litvan, Oscar L. Lopez, Ian R. A. Mackenzie, Mario Masellis, Fodi Massoud, Paige Moorhouse, John C. Morris, Taim Muayqil, Yannick Nadeau, Inger Nennesmo, Jørgen E. Nielsen, Ricardo Nitrini, Sven-Eric Pålhagen, Robert Perry, Gerald Pfeffer, Machiel Pleizier, Steffen Plickert, Gil D. Rabinovici, Philippe H. Robert, Lothar Resch, Gustavo C. Román, Maxime Ros, Pedro Rosa-Neto, Aiman Sanosi, Philip Scheltens, Christian Schmidt, Eric Schmidt, Jean-Paul Soucy, Jette Stokholm, David Summers, Rawan Tarawneh, Louis Verret, Huali Wang, Bengt Winblad, Makoto Yoneda, Xin Yu, Inga Zerr
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