# The Quantum Group \({{\mathrm{GL}}}_q(2)\)

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## Abstract

In this paper, we fix once and for all a field \(\mathbb {K}\). A *ring* (or an *algebra*) means an associative \(\mathbb {K}\)-algebra with unit, not necessarily commutative. It is suggestive to imagine the ring \(A\) as a ring of (polynomial) functions on a space which is an object of noncommutative, or “quantum,” geometry. Morphisms of spaces correspond to ring homomorphisms in the opposite direction. For \(A\) and \(B\) fixed, the set \({{\mathrm{Hom}}}_{\mathbb {K}{-}\mathrm {alg}}(A, B)\) is also called the set of \(B\)-*points of the space* defined by \(A\).

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