Ideal

Ideal may refer to:

In philosophy

In mathematics

In science

Lie algebra

In mathematics, a Lie algebra (/liː/, not /laɪ/) is a vector space together with a non-associative multiplication called "Lie bracket" . It was introduced to study the concept of infinitesimal transformations. Hermann Weyl introduced the term "Lie algebra" (after Sophus Lie) in the 1930s. In older texts, the name "infinitesimal group" is used.

Lie algebras are closely related to Lie groups which are groups that are also smooth manifolds, with the property that the group operations of multiplication and inversion are smooth maps. Any Lie group gives rise to a Lie algebra. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering (Lie's third theorem). This correspondence between Lie groups and Lie algebras allows one to study Lie groups in terms of Lie algebras.

Definitions

A Lie algebra is a vector space over some field F together with a binary operation called the Lie bracket that satisfies the following axioms:

Ideal (album)

Ideal is the eponymous debut album by R&B group Ideal released on August 24, 1999 by Virgin Records US. The first single "Get Gone" was featured on the 1999 compilation album Now That's What I Call Music! 3

The album sold 615,000 units in the U.S., according to Nielsen SoundScan, and was certified Gold by the RIAA. It features the hit single "Get Gone", which reached #13 on the Billboard Hot 100 chart, and the moderately successful third single "Whatever". Allmusic's Heather Phares called Ideal's initial effort a "heartfelt first album" which showcased the "group's smooth, sensuous vocal styling and romantic songwriting.

Track listing

Movement

Movement may refer to:

Society and the arts

Music

She Wolf

She Wolf (Spanish: Loba) is the eighth studio album by Colombian singer-songwriter Shakira. It was released on 9 October 2009, by Epic Records and Sony Music Latin. As executive producers, Shakira and Amanda Ghost enlisted collaborators including The Neptunes, John Hill, Wyclef Jean, Lukas Burton, Future Cut, Jerry Duplessis and Timbaland. Musically, the record shifts from her traditional Latin pop and pop rock musical styles, instead exploring electropop, with influences of folk and world music. The lyrical themes of the album mostly focus on love and relationships and were based on the conversations Shakira had with her friends.

She Wolf reached number one on the charts of Argentina, Ireland, Italy, Mexico and Switzerland. It also charted inside the top five in Spain, Germany and the United Kingdom. It debuted at number fifteen on the Billboard 200. She Wolf was certified double-platinum in Colombia and Mexico, platinum in Italy and Spain, and gold in numerous countries including France and the United Kingdom.

The Pillows

The Pillows (ザ・ピロウズ, stylized as the pillows) are a Japanese alternative rock band formed in 1989. As of 2014, the group has released 19 original studio albums, several EPs and compilations, and over 30 singles. Outside Japan, they are best known as the group responsible for the soundtrack to the FLCL OVA series.

History

Formation and early years (1989-94)

In 1989 Kenji Ueda, bassist for Kenzi & The Trips, left the band with former Kenzi's drummer Shinichiro Sato and invited The Coin Locker Babies vocalist Sawao Yamanaka to form a new band. Since Yamanaka was not able to play the guitar well yet, Yoshiaki Manabe, the guitarist of the hair metal band Persia, joined them. The Pillows were formed on September 16, 1989. The story as to where the band's name came about is that allegedly Sawao Yamanaka was hanging out at Yoshiaki Manabe's place and an English post-punk compilation record entitled Pillows & Prayers hanging on Manabe's wall inspired him.

Ueda and Yamanaka were the main songwriters and The Pillows released their first EPs, Pantomime and 90's My Life in 1990 under Captain Records.