# Dr Phillip Isaac

## Personal page

Dr Phillip Isaac's personal page

## Teaching and learning

Dr Isaac teaches into 2nd and 3rd year mathematics including mathematical analyis, calculus and linear algebra, and partial differential equations.

## Researcher biography

Dr Phillip Isaac is a mathematician interested in algebraic structures, particularly those related to quantum integrable systems.

Phillip received his PhD in mathematics in May 2001 from UQ. The title of his thesis was "Quasi Hopf superalgebras and their dual structures".

He worked as a JAVA programmer/cryptographer for about 9 months before undertaking a postdoctoral research fellowship at the Graduate School of Mathematical Sciences, University of Tokyo, Japan. His project was entitled "Symmetries in quantum spin chains".

After his return to Australia in September 2003, he began casual employment at UQ, working as a first year tutor and developing course materials.

His current research activities involve developing the constructive representation theory of Lie (super)algebras, quantum groups and related structures, and its utility in application, particularly to quantum integrable systems.

### Journal Articles

*A connection between Uq(sl(3)) and Z2×Z2-graded special linear Lie colour algebras via Klein operators*. Journal of Mathematical Physics, 65 (1) ARTN 013503. doi: 10.1063/5.0163904

*Occupancy probabilities in superintegrable bosonic networks*. Nuclear Physics B, 998 116406, 116406. doi: 10.1016/j.nuclphysb.2023.116406

*NOON state measurement probabilities and outcome fidelities: a Bethe Ansatz approach*. Journal of Physics A: Mathematical and Theoretical, 56 (50) 505202, 1-27. doi: 10.1088/1751-8121/ad0a71

*Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras*. Journal of Physics A: Mathematical and Theoretical, 55 (23) 235201, 235201. doi: 10.1088/1751-8121/ac6715

*ℤ2 × ℤ2-Generalizations of Infinite-Dimensional Lie Superalgebra of Conformal Type with Complete Classification of Central Extensions*. Reports on Mathematical Physics, 85 (3), 351-373. doi: 10.1016/S0034-4877(20)30041-0

*Ground-state energy of a Richardson-Gaudin integrable BCS model*. SciPost Physics Core, 2 (1) 001. doi: 10.21468/scipostphyscore.2.1.001

*The Z2×Z2-graded general linear Lie superalgebra*. Journal of Mathematical Physics, 61 (1) 011702, 011702. doi: 10.1063/1.5138597

*Invariants and matrix elements of the quantum group U*. Journal of Physics A: Mathematical and Theoretical, 52 (29) 295201, 295201. doi: 10.1088/1751-8121/ab2676

_{q}[gl(n, C)] revisited*Z2×Z2 generalizations of N=1 superconformal Galilei algebras and their representations*. Journal of Mathematical Physics, 60 (2) 023507, 023507. doi: 10.1063/1.5054699

*On Casimir operators of conformal Galilei algebras*. Journal of Mathematical Physics, 60 (1) 013509, 013509. doi: 10.1063/1.5064840

*Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz*. Nuclear Physics B, 937, 28-55. doi: 10.1016/j.nuclphysb.2018.08.015

*Energy-level crossings and number-parity effects in a bosonic tunneling model*. Journal of Physics B: Atomic, Molecular and Optical Physics, 51 (14) 145301, 145301. doi: 10.1088/1361-6455/aac6f2

*A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras*. Journal of Physics A: Mathematical and Theoretical, 51 (6) 065206, 065206. doi: 10.1088/1751-8121/aaa468

*Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond*. Journal of Physics A: Mathematical and Theoretical, 50 (36) 365202, 365202. doi: 10.1088/1751-8121/aa8119

*Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis*. Physical Review A, 95 (4) 043607. doi: 10.1103/PhysRevA.95.043607

*An integrable case of the p + ip pairing Hamiltonian interacting with its environment*. Journal of Physics A-Mathematical and Theoretical, 49 (8) 084001. doi: 10.1088/1751-8113/49/8/084001

*Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)*. Journal of Mathematical Physics, 56 (12) 121703, 121703-1-121703-19. doi: 10.1063/1.4938076

*Reduced matrix elements of the orthosymplectic Lie superalgebra*. Journal of Physics A: Mathematical and Theoretical, 48 (2) 025201, 1-39. doi: 10.1088/1751-8113/48/2/025201

*On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system*. Nuclear Physics B, 886, 364-398. doi: 10.1016/j.nuclphysb.2014.06.018

*On realizations of polynomial algebras with three generators via deformed oscillator algebras*. Journal of Physics A: Mathematical and Theoretical, 47 (20) 205203, 1-26. doi: 10.1088/1751-8113/47/20/205203

*Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)*. Journal of Mathematical Physics, 55 (011703) 011703, 011703.1-011703.32. doi: 10.1063/1.4861706

*Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)*. Journal of Mathematical Physics, 54 (1) 013505, 013505. doi: 10.1063/1.4773573

*Highest weight representations and Kac determinants for a class of conformal galilei algebras with central extension*. International Journal of Mathematics, 23 (11) 1250118, 1250118.1-1250118.25. doi: 10.1142/S0129167X12501182

*A variational approach for the quantum inverse scattering method*. Inverse Problems, 28 (3) 035008, 035008.1-035008.15. doi: 10.1088/0266-5611/28/3/035008

*BEC-BCS crossover in a (p + ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs*. Nuclear Physics B, 848 (2), 372-397. doi: 10.1016/j.nuclphysb.2011.03.001

*Solutions of the Yang-Baxter equation: Descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras*. Nuclear Physics Section B, 847 (2), 387-412. doi: 10.1016/j.nuclphysb.2011.01.034

*On irreducible representations of the exotic conformal Galilei algebra*. Journal of Physics A-Mathematical and Theoretical, 44 (3) 035401, 1-8. doi: 10.1088/1751-8113/44/3/035401

*Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D-3) symmetry*. Nuclear Physics, Section B, 836 (3), 171-185. doi: 10.1016/j.nuclphysb.2010.04.014

*Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry*. Nuclear Physics B, 812 (3), 456-469. doi: 10.1016/j.nuclphysb.2008.12.002

*Assessment of an innovative system of lecture notes in first-year mathematics*. International Journal of Mathematical Education in Science and Technology, 40 (4), 495-504. doi: 10.1080/00207390902759592

*Universal Baxterization for Z-graded Hopf algebras*. Journal of Physics A: Mathematical and Theoretical, 40 (50), F1069-F1075. doi: 10.1088/1751-8113/40/50/F01

*An algebraic approach to symmetric pre-monoidal statistics*. Journal of Algebra and Its Applications, 6 (1), 49-69. doi: 10.1142/S0219498807002065

*Representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the Yang–Baxter equation*. Journal of Mathematical Physics, 47 (10) 103511, 103511-1-103511-18. doi: 10.1063/1.2359575

*Weak Hopf algebras corresponding to U-q[sl(n)]*. Journal of Mathematical Physics, 44 (11), 5250-5267. doi: 10.1063/1.1616999

*On Quasi-Hopf Superalgebras*. Communications in Mathematical Physics, 224 (2), 341-372. doi: 10.1007/s00220-001-0566-2

*Casimir invariants from quasi-Hopf (super)algebras*. Journal of Mathematical Physics, 41 (1), 547-568. doi: 10.1063/1.533151

### Conference Papers

*Characteristic identities for Lie (super)algebras*.

*30th International Colloquium on Group Theoretical Methods in Physics (Group30)*, Ghent Belgium, 14-18 July, 2014. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/597/1/012045

*Exactly solvable BCS-BEC crossover Hamiltonians*.

*The XXIX International Colloquium on Group-Theoretical Methods in Physics*, Tianjin, China, 20-26 August 2012. Hackensack, NJ, United States: World Scientific. doi: 10.1142/9789814518550_0018

*Introducing a group research project into a second-level mathematics course*.

*UniServe Science Conference 2009*, Sydney, NSW, Australia, 30 September - 2 October 2009. Sydney, NSW, Australia: UniServe Science.

*Ribbon structure in symmetric pre-monoidal categories*.

*XXV International Colloquium on Group Theoretical Methods in*, Cocoyoc, Mexico, 2-6 August, 2004. Bristol, U.K.: Institute of Physics Publishing.

*Quasi-Lie algebras and a method for determining non-degeneracy of the quasi-Lie product*.

*12th International Colloquium on Group Theoretical Methods in Physics (Group 22)*, Hobart Australia, Jul 13-17, 1998. CAMBRIDGE: INTERNATIONAL PRESS INC BOSTON.

### Thesis

*Quasi Hopf superalgebras and their dual structures*. PhD Thesis, School of Physical Sciences, The University of Queensland. doi: 10.14264/uql.2019.664