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Second Life also has its own virtual currency, the Linden Dollar (L$), which is exchangeable with real world currency. [14] [15] Second Life is intended for people ages 16 and over, with the exception of 13–15-year-old users, who are restricted to the Second Life region of a sponsoring institution (e.g., a school). [16] [17]
The group SL(2, R) acts on its Lie algebra sl(2, R) by conjugation (remember that the Lie algebra elements are also 2 × 2 matrices), yielding a faithful 3-dimensional linear representation of PSL(2, R). This can alternatively be described as the action of PSL(2, R) on the space of quadratic forms on R 2. The result is the following representation:
It generates the center of the universal enveloping algebra of the complexified Lie algebra of SL(2, R). The Casimir element acts on any irreducible representation as multiplication by some complex scalar μ 2. Thus in the case of the Lie algebra sl 2, the infinitesimal character of an irreducible representation is specified by one complex number.
[2] OpenSimulator uses loadable modules for most of its functionality. These loadable modules can be independently developed to add functionality to the server. [3] OpenSimulator currently uses a modified Second Life protocol for client to server communication, and requires retrofitting to a suitable virtual world viewer (client) in order to ...
Residents may purchase L$ directly through the Second Life viewer, or by logging into the website and using the Lindex Exchange. The ratio of L$ to US$ (L$: US$) is a floating exchange rate depending on supply and demand; Linden Dollars can be purchased and sold on the Lindex at the current market rate, or residents can set their own limit to get a better exchange rate.
Don’t call The Real Housewives of Salt Lake City star Heather Gay a mean girl. Andy Cohen read a fan question during the RHOSLC season 5 reunion on Wednesday, January 22, in which the viewer ...
In 1973, Pierre Deligne and Michael Rapoport showed that the ring of modular forms M(Γ) is finitely generated when Γ is a congruence subgroup of SL(2, Z). [2]In 2003, Lev Borisov and Paul Gunnells showed that the ring of modular forms M(Γ) is generated in weight at most 3 when is the congruence subgroup () of prime level N in SL(2, Z) using the theory of toric modular forms. [3]
The algebra plays an important role in the study of chaos and fractals, as it generates the Möbius group SL(2,R), which describes the automorphisms of the hyperbolic plane, the simplest Riemann surface of negative curvature; by contrast, SL(2,C) describes the automorphisms of the hyperbolic 3-dimensional ball.