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Information about Anyline OCR SDK including independent reviews; ratings. Comparisons; alternatives to Anyline OCR SDK from other OCR. In the same way, one de nes a real Lie algebra as a real vector space with an antisymmetric bracket [ , ] that satis es the Jacobi identity The two concepts are closely related If g is a real Lie algebra, one can de ne its complexi cation gc by complexifying it as a vector space and extending the Lie bracket by linearity If dim g = n, the complex dimension of gc is still n, but its real dimension is 2n Conversely, if g is a complex Lie algebra, and one restricts its parameter space to real numbers, one obtains a real form gr , that is, a real Lie algebra whose complexi cation is again g A given complex Lie algebra has in general several nonisomorphic real forms (also classi ed by Cartan), among them a unique compact one, characterized by the fact that the Cartan Killing metric g i j is negative-de nite For instance, the complex Lie algebra A2 yields two real forms, su(3), the compact one, and su(2, 1) For physical applications, it is not so much the Lie algebras themselves that matter, but their representations in Hilbert spaces The key ingredient for building the latter, also due to Cartan, is the notion of a weight vector Let T be a representation of the Lie algebra g in the Hilbert space h, that is, a linear map of g into the operators on h such that T ([X , Y ]) = [T (X ), T (Y )] , X,Y g (B9) free ocr sdk Asprise OCR SDK Developers Guide | Thread (Computing) | License
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