Context and question: Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple models—imposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v[›] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter serves—in the absence of significant gravitation—as a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincaré group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
What is important to Lie groups?
Answer: unanswerable
Context and question: As many as five bands were on tour during the 1920s. The Jenkins Orphanage Band played in the inaugural parades of Presidents Theodore Roosevelt and William Taft and toured the USA and Europe. The band also played on Broadway for the play "Porgy" by DuBose and Dorothy Heyward, a stage version of their novel of the same title. The story was based in Charleston and featured the Gullah community. The Heywards insisted on hiring the real Jenkins Orphanage Band to portray themselves on stage. Only a few years later, DuBose Heyward collaborated with George and Ira Gershwin to turn his novel into the now famous opera, Porgy and Bess (so named so as to distinguish it from the play). George Gershwin and Heyward spent the summer of 1934 at Folly Beach outside of Charleston writing this "folk opera", as Gershwin called it. Porgy and Bess is considered the Great American Opera[citation needed] and is widely performed.
What was the name of the "folk opera" based on 'Porgy'?
Answer: Porgy and Bess
Context and question: Asian Americans in New York City, according to the 2010 Census, number more than one million, greater than the combined totals of San Francisco and Los Angeles. New York contains the highest total Asian population of any U.S. city proper. The New York City borough of Queens is home to the state's largest Asian American population and the largest Andean (Colombian, Ecuadorian, Peruvian, and Bolivian) populations in the United States, and is also the most ethnically diverse urban area in the world. The Chinese population constitutes the fastest-growing nationality in New York State; multiple satellites of the original Manhattan Chinatown (紐約華埠), in Brooklyn (布鲁克林華埠), and around Flushing, Queens (法拉盛華埠), are thriving as traditionally urban enclaves, while also expanding rapidly eastward into suburban Nassau County (拿騷縣) on Long Island (長島), as the New York metropolitan region and New York State have become the top destinations for new Chinese immigrants, respectively, and large-scale Chinese immigration continues into New York City and surrounding areas. In 2012, 6.3% of New York City was of Chinese ethnicity, with nearly three-fourths living in either Queens or Brooklyn, geographically on Long Island. A community numbering 20,000 Korean-Chinese (Chaoxianzu (Chinese: 朝鲜族) or Joseonjok (Hangul: 조선족)) is centered in Flushing, Queens, while New York City is also home to the largest Tibetan population outside China, India, and Nepal, also centered in Queens. Koreans made up 1.2% of the city's population, and Japanese 0.3%. Filipinos were the largest Southeast Asian ethnic group at 0.8%, followed by Vietnamese, who made up 0.2% of New York City's population in 2010. Indians are the largest South Asian group, comprising 2.4% of the city's population, with Bangladeshis and Pakistanis at 0.7% and 0.5%, respectively. Queens is the preferred borough of settlement for Asian Indians, Koreans, and Filipinos, as well as Malaysians and other Southeast Asians; while Brooklyn is receiving large numbers of both West Indian as well as Asian Indian immigrants.
What borough housed the first Chinatown in New York?
Answer:
Manhattan