SO(8)

In mathematics, SO(8) is the special orthogonal group acting on eight-dimensional Euclidean space. It could be either a real or complex simple Lie group of rank 4 and dimension 28.

Spin(8)

Like all special orthogonal groups of , SO(8) is not simply connected, having a fundamental group isomorphic to Z₂. The universal cover of SO(8) is the spin group Spin(8).

Center

The center of SO(8) is Z₂, the diagonal matrices {±I} (as for all SO(2n) for 2n > 2), while the center of Spin(8) is Z₂×Z₂ (as for all Spin(4n), 4n > 0).

Triality

SO(8) is unique among the simple Lie groups in that its Dynkin diagram (shown right) (D₄ under the Dynkin classification) possesses a three-fold symmetry. This gives rise to peculiar feature of Spin(8) known as triality. Related to this is the fact that the two spinor representations, as well as the fundamental vector representation, of Spin(8) are all eight-dimensional (for all other spin groups the spinor representation is either smaller or larger than the vector representation). The triality automorphism of Spin(8) lives in the outer automorphism group of Spin(8) which is isomorphic to the symmetric group S₃ that permutes these three representations. The automorphism group acts on the center Z₂ x Z₂ (which also has automorphism group isomorphic to S₃ which may also be considered as the general linear group over the finite field with two elements, S₃ ≅GL(2,2)). When one quotients Spin(8) by one central Z₂, breaking this symmetry and obtaining SO(8), the remaining outer automorphism group is only Z₂. The triality symmetry acts again on the further quotient SO(8)/Z₂.

Spin (Darren Hayes album)

Spin is the first solo album released by ex-Savage Garden member Darren Hayes. The album was mixed by Chris Lord-Alge and produced by Walter Afanasieff. It was released in Australia in March 2002 and reached the rest of the world later that year. The album has sold over two million copies as of 2011.

Background

Hayes, continuing the trend from his years as Savage Garden's frontman, addresses romance on almost every track on the album. Walter Afanasieff, who had already worked on Savage Garden's Affirmation, oversaw the production of the majority of the album, with help from co-producers Greg Bieck, Rick Nowels and Robert Conley. Afanasieff produced five of the twelve tracks on the original release: "Insatiable", "Heart Attack", "Dirty", "Good Enough" and the title track, "Spin"; Bieck produced "Strange Relationship" and "I Miss You"; Nowels produced "Creepin' Up on You", "I Can't Ever Get Enough of You", "Like It or Not" and "What You Like"; and Conley solely produced the track "Crush (1980 Me)". Afanasieff also produced the Australian only bonus track, "The Heart Wants What It Wants", and the UK Collector's Edition bonus tracks, "I Wish U Heaven" and "Can't Help Falling in Love". Till 2006,the album sold 118,000 in United States.

Spin (Lifehouse song)

"Spin" is a song by American alternative rock band Lifehouse from their 2002 album, Stanley Climbfall. It was written by Jason Wade and produced by Ron Aniello. The song received positive reviews from music critics and peaked at #71 on the Billboard Hot 100 chart.

Background

"Spin" is four minutes and 52 seconds long. It was produced by Ron Aniello. Jason Wade, the band's vocalist, wrote the song when he was 16.

Release

"Spin" was the first track on Lifehouse's album Stanley Climbfall, which was released on August 17, 2002. It was also the first single from the album.

Critical reception

The song received positive critical reviews. Gene Stout of the Seattle Post-Intelligencer described it as "an anthemic tune with a strong hook and a big guitar sound."Billboard's Chuck Taylor wrote that "'Spin' is a wonderfully constructed rock song with a number of different musical subsections, all of which showcase the potent pipes and song-writing skills of lead singer/guitarist Jason Wade ... Lifehouse has managed to drum up a keen balance between pure, guitar-fueled rock and hook-sodden, creatively executed pop – and this song deserves a lengthy stay on the playlists of both formats."

Spin (1995 film)

Spin is a 1995 documentary film by Brian Springer composed of raw satellite feeds featuring politicians' pre-appearance planning. It covers, not only the presidential election, but also the 1992 Los Angeles riots as well as the Operation Rescue abortion protests.

Using the 1992 presidential election as his springboard, Springer captures the behind-the-scenes maneuverings of politicians and newscasters in the early 1990s. Pat Robertson banters about "homos," Al Gore learns how to avoid abortion questions, George H. W. Bush talks to Larry King about Halcion—all presuming they're off camera. Composed of 100% unauthorized satellite footage, Spin is a surreal expose of media-constructed reality.

The film documents behind the scenes footage of Larry Agran who unsuccessfully sought the Democratic Party nomination for President. Agran was generally ignored by the media during his candidacy, a topic covered in the documentary. The media did not report his polling numbers even as he met or exceeded the support of other candidates such as Jerry Brown. Party officials excluded him from most debates on various grounds, even having him arrested when he interrupted to ask to participate. When he managed to join the other candidates in any forum, his ideas went unreported.