Split

Quilapayn's path has been marked by internal issues over the years, with some members leaving and others taking their place. In 1987 Willy Oddo, its most charismatic member, decided to leave France to be closer to Chile. He chose to live in Argentina. In October 1988, Pinochet was overthrown by a referendum. After 15 years of exile Quilapayun could return to Chile and performed tours in 1988, 1989, 1991 and 1992. In 1989 Eduardo Carrasco returned to Chile while most of the group continued to live in France and perform around the world. In November 1991 Willy Oddo was murdered by an offender in Santiago. After Rodolfo Parada registered the name "Quilapayn" without the authorization of the other members, other historic members refused to continue with Parada and Wang, resulting in the group splitting into two, both claiming the name and legacy of Quilapayn, and leading to subsequent litigation. The Chile-based historic faction is celebrating the group's 40 year anniversary performing concerts in Chile, Latin America and Europe, together with the "historic" version of Inti-Illimani, another important Chilean group. These joint concerts have been advertised and promoted as IntiQuila. The current "historic" lineup includes Eduardo Carrasco, Rubn Escudero, Ricardo Venegas, Guillermo Garca, Ismael Odd (son of Guillermo "Willy" Odd), Hugo Lagos, Hernn Gmez, Carlos Quezada and Sebastin Quezada (son of Carlos). On December 5, 2007, the Court of Appeal of Paris forbade Parada and Wang's group "from making use of the name QUILAPAYN, subject to a fine of 10 000 euros per infringement". This judgement was confirmed by the Highest Court of Appeal (Cour de Cassation de Paris) on June 11, 2009. In 2015 the band's career reached its fiftieth year and both factions celebrated this anniversary. Parada's group performed three big shows at the end August in Santiago, together with other well-known Chilean artists while the "historic" faction made a big concert in front of Palacio de la Moneda in Santiago and announced several other anniversary concerts in Chile, Colombia and Spain on its website. In November 2015, the Chilean trademark conflict ended, since the Instituto Nacional de Patentes Industriales (INAPI), after a thirteen years process gave the exclusive right for using the mark "Quilapayun" to the group headed by Carrasco.

• Other Related Knowledge ofa split

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Non-split reductive groups

As discussed above, the classification of split reductive groups is the same over any field. By contrast, the classification of arbitrary reductive groups can be hard, depending on the base field. Some examples among the classical groups are: Every nondegenerate quadratic form q over a field k determines a reductive group G = SO(q). Here G is simple if q has dimension n at least 3, since G k displaystyle G_overline k is isomorphic to SO(n) over an algebraic closure k displaystyle overline k . The k-rank of G is equal to the Witt index of q (the maximum dimension of an isotropic subspace over k). So the simple group G is split over k if and only if q has the maximum possible Witt index, n / 2 displaystyle lfloor n/2

floor . Every central simple algebra A over k determines a reductive group G = SL(1,A), the kernel of the reduced norm on the group of units A* (as an algebraic group over k). The degree of A means the square root of the dimension of A as a k-vector space. Here G is simple if A has degree n at least 2, since G k displaystyle G_overline k is isomorphic to SL(n) over k displaystyle overline k . If A has index r (meaning that A is isomorphic to the matrix algebra Mn/r(D) for a division algebra D of degree r over k), then the k-rank of G is (n/r) 1. So the simple group G is split over k if and only if A is a matrix algebra over k.As a result, the problem of classifying reductive groups over k essentially includes the problem of classifying all quadratic forms over k or all central simple algebras over k. These problems are easy for k algebraically closed, and they are understood for some other fields such as number fields, but for arbitrary fields there are many open questions. A reductive group over a field k is called isotropic if it has k-rank greater than 0 (that is, if it contains a nontrivial split torus), and otherwise anisotropic. For a semisimple group G over a field k, the following conditions are equivalent: G is isotropic (that is, G contains a copy of the multiplicative group Gm over k); G contains a parabolic subgroup over k not equal to G; G contains a copy of the additive group Ga over k.For k perfect, it is also equivalent to say that G(k) contains a unipotent element other than 1. For a connected linear algebraic group G over a local field k of characteristic zero (such as the real numbers), the group G(k) is compact in the classical topology (based on the topology of k) if and only if G is reductive and anisotropic. Example: the orthogonal group SO(p,q) over R has real rank min(p,q), and so it is anisotropic if and only if p or q is zero. A reductive group G over a field k is called quasi-split if it contains a Borel subgroup over k. A split reductive group is quasi-split. If G is quasi-split over k, then any two Borel subgroups of G are conjugate by some element of G(k). Example: the orthogonal group SO(p,q) over R is split if and only if |pq| 1, and it is quasi-split if and only if |pq| 2.