Dr Unger's research interests are in the areas of quadratic and hermitian forms, central simple algebras with an involution and non-associative algebras. Key players in his research are the (generalized) quaternion algebras discovered by Hamilton in 1843 and their Cayley-Dickson doubles, the octonion algebras. His recent investigations involve the extension of important quadratic form theoretic local-global principles to the (mostly) non-commutative realm of hermitian forms over division algebras.
Main publications:
Recent Publications
David W. Lewis, Thomas Unger and Jan Van Geel, The Hasse principle for similarity of hermitian forms, J. Algebra 285 (2005), 196-212.
Susanne Pumpluen and Thomas Unger, The hermitian level of composition algebras, manuscripta mathematica 109 (2002), 511-525.
David W. Lewis and Thomas Unger, A local-global principle for algebras with involution and hermitian forms, Math. Zeit. 244 (2003), 469-477.
David W. Lewis, Claus Scheiderer and Thomas Unger, A weak Hasse principle for central simple algebras with an involution, Doc. Math. Extra Volume, Proc. Conf. Quadratic Forms and Related Topics, Baton Rouge, La., 2001, 241-251 (2001)
Thomas Unger, Clifford algebra periodicity for central simple algebras with an involution, Comm. Algebra, 29(3) (2001), 1141--1152.
