In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication.
In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
In art a predella (plural predelle) is the lowest part of an altarpiece, sometimes forming a platform or step, and the painting or sculpture along it, at the bottom of an altarpiece, sometimes with a single much larger main scene above, but often (especially in earlier examples), a polyptych or multipanel altarpiece. In late medieval and Renaissance altarpieces, where the main panel consisted of a scene with large figures, it was normal to include a predella below with a number of small-scale narrative paintings depicting events from the life of the dedicatee, whether the Life of Christ, the Life of the Virgin or a saint. Typically there would be three to five small scenes, in a horizontal format. Sometimes a single space shows different scenes in continuous representation.
They are significant in art history, as the artist had more freedom from iconographic conventions than in the main panel as they could only be seen from close up. As the main panels themselves became larger and more dramatic, predellas fell from use around 1510-20 in the High Renaissance, although older or more conservative painters continued to use them, for example Luca Signorelli, by then in his 70s, in about 1521. In this case he is thought to have only done the underdrawing for the main scene, leaving the painting to his workshop assistants. But he is thought to have painted the predella scenes himself.
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