Mathematics
Seminar
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Rocky Mountain Algebraic Combinatorics Seminar
Automorphic Loops: A Survey and Recent Progress
Michael Kinyon
University of Denver
The multiplication group Mlt(G) of a group G is just the
permutation group generated by all left and right translations, which is
essentially what you get when you think of both the left and right regular
representations simultaneously. The inner automorphism group
Inn(G) can then be characterized as the stabilizer in
Mlt(G) of the identity element of G.
In the nonassociative world, if
Q is a loop, then the same definitions
give the multiplication group
Mlt(
Q) and the inner mapping group
Inn(
Q), but the latter does not necessarily act as automorphisms
of Q. A loop is said to be
automorphic if every inner mapping is an
automorphism. Thus automorphic loops include groups but much more that.
This talk will start with a survey of automorphic loops, including a potted
history and ending with the current state of the art. The main open problem
is the existence or nonexistence of a finite, simple, nonassociative,
automorphic loop, and I will talk about results both published and
unpublished regarding them.
On the classification of involutory latin quandles
Petr Vojt\v{e}chovsk\'y
University of Denver
Quandles are binary algebras designed for colorings of arcs in knot diagrams
that are invariant under Reidemeister moves. Quandles also solve the quantum
Yang-Baxter equation. It is therefore of considerable interest to construct
well-structured families of quandles. In this talk I will present a
classification of involutory latin quandles of order p*q (using group
actions on periodic sequences over finite fields) and also a computer
enumeration of involutory latin quandles of odd prime power order (using
central extensions).
Weber 223
4–6 pm
Friday, November 10, 2017
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University
This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly.
Anyone interested is welcome to join us at a local restaurant for dinner after the talks.
PDF version
Previous Seminars:
- October 20, 2017
- Eric Moorhouse,
William DeMeo
- October 6, 2017
- Spencer Gerhardt,
Joshua Grochow
- September 22, 2017
- Amanda Schaeffer Fry,
Henry Kvinge
- September 8, 2017
- Peter Mayr,
James B. Wilson
- May 5, 2017
- Ferdinand Ihringer,
Gavin King
- April 21, 2017
- Vladimir D. Tonchev,
Morgan Rodgers
- April 7, 2017
- Jason Williford,
Anton Betten
- March 24, 2017
- Isabella Novik,
Peter Brooksbank
- March 3, 2017
- Jintai Ding,
Curtis Bennett
- February 17, 2017
- Fatma Karaoglu,
Eric Moorhouse
- February 3, 2017
- Tim Penttila,
James B. Wilson
- December 2, 2016
- Jim Fowler,
Andrew Kelley
- November 11, 2016
- Joseph Gersch,
Joshua Maglione
- October 28, 2016
- John MacLaren Walsh,
Henry Adams
- October 14, 2016
- JM Landsberg,
James B. Wilson
- September 30, 2016
- Alexander Hulpke,
Oscar Levin
- September 16, 2016
- Delaram Kahrobaei,
Amit Patel
- June 23, 2016
- Jason Cantarella,
Michal Adamaszek
- April 29, 2016
- Nick Loehr,
Jason Williford
- April 15, 2016
- Alexander Hulpke,
Klaus Lux
- April 1, 2016
- Eamonn O'Brien,
Izabella Stuhl
- February 19, 2015
- James Wilson,
Anton Betten
- December 4, 2015
- Maria Monks Gillespie,
Dane Flannery
- November 13, 2015
- Richard Green,
Tim Penttila
- October 23, 2015
- Christina Boucher,
Sylvia Hobart
- October 9, 2015
- Josh Maglione,
Ghodratollah Aalipour
- September 25, 2015
- Ross McConnell,
Henry Adams
- September 11, 2015
- James B. Wilson,
Tim Penttila
- May 8, 2015
- Amanda Schaeffer Fry,
Peter Brooksbank
- April 24, 2015
- Heide Gluesing-Luerssen,
Phil DeOrsey
- March 6, 2015
- Felice Manganiello,
Eric Moorhouse
- February 20, 2015
- Anton Dzhamay,
Anton Betten
- February 6, 2015
- Alexander Hulpke,
Morgan Rodgers
- December 5, 2014
- Stefaan De Winter,
Gretchen Matthews
- November 14, 2014
- Greg Coxson,
Tom Dorsey
- October 31, 2014
- Octavio Paez Osuna,
Sylvia Hobart
- October 10, 2014
- Takunari Miyazaki,
Eric Moorhouse
- September 26, 2014
- Elissa Ross,
Anton Betten
- September 12, 2014
- Petr Vojtěchovský,
Alexander Hulpke
- May 9, 2014
- Philip DeOrsey,
Tim Penttila
- April 25, 2014
- William J Martin,
Jason Williford
- April 11, 2014
- Victor Pambuccian,
George Shakan
- March 7, 2014
- Nathan Lindzey,
Jens Harlander
- February 21, 2014
- Ross McConnell,
Anton Betten
- November 22, 2013
- Justin Hughes,
Josh Maglione
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Department of Mathematics
Fort Collins, Colorado 80523
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