### Tropical matrix algebra (Marianne Johnson, NBSAN York, 25th November 2009)

**Abstract:**
Tropical algebra (also known as max-plus algebra) is the linear algebra of
the real numbers augmented with minus infinity when equipped with the binary
operations of addition and maximisation. In this talk I shall describe some
joint work with Mark Kambites on the algebraic structure of the semigroup of
all 2x2 tropical matrices under multiplication. In particular, we
give a complete description of Green's relations and the maximal subgroups
of this semigroup.